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Vasilopoulos A, Fytas NG, Vatansever E, Malakis A, Weigel M. Universality in the two-dimensional dilute Baxter-Wu model. Phys Rev E 2022; 105:054143. [PMID: 35706204 DOI: 10.1103/physreve.105.054143] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/09/2022] [Accepted: 05/02/2022] [Indexed: 06/15/2023]
Abstract
We study the question of universality in the two-dimensional spin-1 Baxter-Wu model in the presence of a crystal field Δ. We employ extensive numerical simulations of two types, providing us with complementary results: Wang-Landau sampling at fixed values of Δ and a parallelized variant of the multicanonical approach performed at constant temperature T. A detailed finite-size scaling analysis in the regime of second-order phase transitions in the (Δ,T) phase diagram indicates that the transition belongs to the universality class of the four-state Potts model. Previous controversies with respect to the nature of the transition are discussed and attributed to the presence of strong finite-size effects, especially as one approaches the pentacritical point of the model.
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Affiliation(s)
| | - Nikolaos G Fytas
- Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, United Kingdom
- Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
| | - Erol Vatansever
- Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, United Kingdom
- Department of Physics, Dokuz Eylül University, TR-35160 Izmir, Turkey
| | - Anastasios Malakis
- Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, United Kingdom
- Department of Physics, University of Athens, Panepistimiopolis, GR-15784 Zografou, Greece
| | - Martin Weigel
- Institut für Physik, Technische Universität Chemnitz, D-09107 Chemnitz, Germany
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2
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Generalized Gibbs Phase Rule and Multicriticality Applied to Magnetic Systems. ENTROPY 2021; 24:e24010063. [PMID: 35052088 PMCID: PMC8775071 DOI: 10.3390/e24010063] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 11/15/2021] [Revised: 12/20/2021] [Accepted: 12/27/2021] [Indexed: 11/17/2022]
Abstract
A generalization of the original Gibbs phase rule is proposed in order to study the presence of single phases, multiphase coexistence, and multicritical phenomena in lattice spin magnetic models. The rule is based on counting the thermodynamic number of degrees of freedom, which strongly depends on the external fields needed to break the ground state degeneracy of the model. The phase diagrams of some spin Hamiltonians are analyzed according to this general phase rule, including general spin Ising and Blume–Capel models, as well as q-state Potts models. It is shown that by properly taking into account the intensive fields of the model in study, the generalized Gibbs phase rule furnishes a good description of the possible topology of the corresponding phase diagram. Although this scheme is unfortunately not able to locate the phase boundaries, it is quite useful to at least provide a good description regarding the possible presence of critical and multicritical surfaces, as well as isolated multicritical points.
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3
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Naskar M, Acharyya M, Vatansever E, Fytas NG. Metastable behavior of the spin-s Ising and Blume-Capel ferromagnets: A Monte Carlo study. Phys Rev E 2021; 104:014107. [PMID: 34412250 DOI: 10.1103/physreve.104.014107] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2021] [Accepted: 06/14/2021] [Indexed: 06/13/2023]
Abstract
We present an extensive Monte Carlo investigation of the metastable lifetime through the reversal of the magnetization of spin-s Ising and Blume-Capel models, where s={1/2,1,3/2,2,5/2,3,7/2}. The mean metastable lifetime (or reversal time) is studied as a function of the applied magnetic field, and for both models it is found to obey the Becker-Döring theory, as was initially developed for the case of an s=1/2 Ising ferromagnet within the classical nucleation theory. Moreover, the decay of the metastable volume fraction nicely follows Avrami's law for all values of s and for both models considered.
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Affiliation(s)
- Moumita Naskar
- Department of Physics, Presidency University, 86/1 College Street, Kolkata-700073, India
| | - Muktish Acharyya
- Department of Physics, Presidency University, 86/1 College Street, Kolkata-700073, India
| | - Erol Vatansever
- Department of Physics, Dokuz Eylül University, TR-35160 Izmir, Turkey and Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, United Kingdom
| | - Nikolaos G Fytas
- Centre for Fluid and Complex Systems, Coventry University, Coventry CV1 5FB, United Kingdom
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4
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Carvalho DC, Plascak JA. Thermodynamic properties of the spin S=3/2 quantum ferromagnetic Blume-Capel model in a transverse crystal field. Phys Rev E 2021; 103:032142. [PMID: 33862702 DOI: 10.1103/physreve.103.032142] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/06/2021] [Accepted: 03/11/2021] [Indexed: 11/07/2022]
Abstract
The thermodynamic properties of the spin S=3/2 ferromagnetic Ising model in the presence of transverse and longitudinal crystal fields (equivalent to the Blume-Capel model with a transverse crystal field) have been studied by using two different approaches: (i) a zero-temperature mapping of the system onto a spin-1/2 quantum Ising model in longitudinal and transverse fields, together with time-independent quantum perturbation theory; and (ii) a standard mean-field approximation within the framework of the Bogoliubov inequality for the free energy. A very rich phase diagram, with different kinds of multicritical behavior, has been obtained. The results show first- and second-order transition lines, tricritical and tetracritical points, critical end points with a two-phase coexistence, double critical end points, and also double noncritical end points. Additionally, the behavior of the magnetization as a function of temperature, over a wide range of values of both longitudinal and transverse crystal fields, has also been analyzed in detail. While large magnitudes of the longitudinal crystal field select the z-spin components either in their states ±3/2 or ±1/2, it is surprising that a large transverse crystal field induces the spin component in the z direction to values ±1, which are completely different from any expected natural component. This comes indeed as a result of the zero-temperature mapping of the ground state with the superposition of the states 3/2 and -1/2, in one sector of the Hilbert space, and the states -3/2 and 1/2 on the other disjoint sector of the Hilbert space. This superposition for a large transverse crystal field prevails even for finite temperatures, implying that the exact critical points are obtained for the model on the one-dimensional lattice and the two-dimensional square lattice, and quite accurate estimates can be achieved for the three-dimensional simple cubic lattice.
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Affiliation(s)
- D C Carvalho
- Instituto Federal do Norte de Minas Gerais, Campus Salinas, MG, CEP 39560-000, Brazil
| | - J A Plascak
- Departamento de Física, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970, Belo Horizonte-MG, Brazil.,Departamento de Física, Universidade Federal da Paraíba, Caixa Postal 5008, 58051-900, João Pessoa-PB, Brazil.,Department of Physics and Astronomy, University of Georgia, Athens, Georgia 30602, USA
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5
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Sumedha, Mukherjee S. Emergence of a bicritical end point in the random-crystal-field Blume-Capel model. Phys Rev E 2020; 101:042125. [PMID: 32422747 DOI: 10.1103/physreve.101.042125] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/16/2019] [Accepted: 03/20/2020] [Indexed: 11/07/2022]
Abstract
We obtain the phase diagram for the Blume-Capel model with the bimodal distribution for random crystal fields, in the space of three fields: temperature (T), crystal field (Δ), and magnetic field (H) on a fully connected graph. We find three different topologies for the phase diagram, depending on the strength of disorder. Three critical lines meet at a tricritical point only for weak disorder. As disorder strength increases there is no tricritical point in the phase diagram. We instead find a bicritical end point, where only two of the critical lines meet on a first-order surface in the H=0 plane. For intermediate strengths of disorder, the phase diagram has critical end points along with the bicritical end point. One needs to look at the phase diagram in the space of three fields to identify various such multicritical points.
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Affiliation(s)
- Sumedha
- School of Physical Sciences, National Institute of Science Education and Research, Jatni 752050, India and Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
| | - Soheli Mukherjee
- School of Physical Sciences, National Institute of Science Education and Research, Jatni 752050, India and Homi Bhabha National Institute, Training School Complex, Anushakti Nagar, Mumbai 400094, India
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6
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Dias DA, Xavier JC, Plascak JA. Critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field. Phys Rev E 2017; 95:012103. [PMID: 28208359 DOI: 10.1103/physreve.95.012103] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2016] [Indexed: 11/07/2022]
Abstract
The phase diagram and the critical behavior of the spin-1 and the spin-3/2 two-dimensional Baxter-Wu model in a crystal field are studied by conventional finite-size scaling and conformal invariance theory. The phase diagram of this model, for the spin-1 case, is qualitatively the same as those of the diluted 4-states Potts model and the spin-1 Blume-Capel model. However, for the present case, instead of a tricritical point one has a pentacritical point for a finite value of the crystal field, in disagreement with previous work based on finite-size calculations. On the other hand, for the spin-3/2 case, the phase diagram is much richer and can present, besides a pentacritical point, an additional multicritical end point. Our results also support that the universality class of the critical behavior of the spin-1 and spin-3/2 Baxter-Wu model in a crystal field is the same as the pure Baxter-Wu model, even at the multicritical points.
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Affiliation(s)
- D A Dias
- Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970 Belo Horizonte, Minas Gerais, Brazil.,Universidade Federal de Uberlândia, Campus Patos de Minas, Av. Getúlio Vargas 230, 38700-103 Patos de Minas, Minas Gerais, Brazil
| | - J C Xavier
- Instituto de Física, Universidade Federal de Uberlândia, Caixa Postal 593, 38400-902 Uberlândia, Minas Gerais, Brazil
| | - J A Plascak
- Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Caixa Postal 702, 30123-970 Belo Horizonte, Minas Gerais, Brazil.,Universidade Federal da Paraíba, Centro de Ciências Exatas e da Natureza, Campus I, Departamento de Física, CCEN Cidade Universitária, 58051-970 João Pessoa, Paraíba, Brazil.,Center for Simulational Physics, University of Georgia, Athens, Georgia 30602, USA
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7
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Yunus Ç, Renklioğlu B, Keskin M, Berker AN. Stepwise positional-orientational order and the multicritical-multistructural global phase diagram of the s=3/2 Ising model from renormalization-group theory. Phys Rev E 2016; 93:062113. [PMID: 27415214 DOI: 10.1103/physreve.93.062113] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2016] [Indexed: 11/07/2022]
Abstract
The spin-3/2 Ising model, with nearest-neighbor interactions only, is the prototypical system with two different ordering species, with concentrations regulated by a chemical potential. Its global phase diagram, obtained in d=3 by renormalization-group theory in the Migdal-Kadanoff approximation or equivalently as an exact solution of a d=3 hierarchical lattice, with flows subtended by 40 different fixed points, presents a very rich structure containing eight different ordered and disordered phases, with more than 14 different types of phase diagrams in temperature and chemical potential. It exhibits phases with orientational and/or positional order. It also exhibits quintuple phase transition reentrances. Universality of critical exponents is conserved across different renormalization-group flow basins via redundant fixed points. One of the phase diagrams contains a plastic crystal sequence, with positional and orientational ordering encountered consecutively as temperature is lowered. The global phase diagram also contains double critical points, first-order and critical lines between two ordered phases, critical end points, usual and unusual (inverted) bicritical points, tricritical points, multiple tetracritical points, and zero-temperature criticality and bicriticality. The four-state Potts permutation-symmetric subspace is contained in this model.
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Affiliation(s)
- Çağın Yunus
- Department of Physics, Boğaziçi University, Bebek 34342, Istanbul, Turkey
| | - Başak Renklioğlu
- College of Sciences, Koç University, Sarıyer 34450, Istanbul, Turkey.,Department of Physics, Bilkent University, Bilkent 06533, Ankara, Turkey
| | - Mustafa Keskin
- Department of Physics, Erciyes University, Kayseri 38039, Turkey
| | - A Nihat Berker
- Faculty of Engineering and Natural Sciences, Sabancı University, Tuzla 34956, Istanbul, Turkey.,Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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8
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Neto MA, de Sousa JR, Branco NS. Magnetization plateaus in the antiferromagnetic Ising chain with single-ion anisotropy and quenched disorder. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:052153. [PMID: 26066165 DOI: 10.1103/physreve.91.052153] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/18/2015] [Indexed: 06/04/2023]
Abstract
We have studied the presence of plateaus on the low-temperature magnetization of an antiferromagnetic spin-1 chain, as an external uniform magnetic field is varied. A crystal-field interaction is present in the model and the exchange constants follow a random quenched (Bernoulli or Gaussian) distribution. Using a transfer-matrix technique we calculate the largest Lyapunov exponent and, from it, the magnetization at low temperatures as a function of the magnetic field, for different values of the crystal field and the width of the distributions. For the Bernoulli distribution, the number of plateaus increases, with respect to the uniform case [Litaiff et al., Solid State Commun. 147, 494 (2008)] and their presence can be linked to different ground states, when the magnetic field is varied. For the Gaussian distributions, the uniform scenario is maintained, for small widths, but the plateaus structure disappears as the width increases.
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Affiliation(s)
- Minos A Neto
- Departamento de Física, Universidade Federal do Amazonas, 3000, Japiim, 69077-000, Manaus, Amazonas, Brazil
| | - J Ricardo de Sousa
- Departamento de Física, Universidade Federal do Amazonas, 3000, Japiim, 69077-000, Manaus, Amazonas, Brazil and National Institute of Science and Technology for Complex Systems, 3000, Japiim, 69077-000, Manaus, Amazonas, Brazil
| | - N S Branco
- Departamento de Física, Universidade Federal de Santa Catarina, 88040-900, Florianópolis, Santa Catarina, Brazil
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9
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Freire RTS, Plascak JA. Bicritical universality of the anisotropic Heisenberg model in a crystal field. Phys Rev E 2015; 91:032146. [PMID: 25871093 DOI: 10.1103/physreve.91.032146] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/17/2014] [Indexed: 11/07/2022]
Abstract
The bicritical properties of the three-dimensional classical anisotropic Heisenberg model in a crystal field are investigated through extensive Monte Carlo simulations on a simple cubic lattice, using Metropolis and Wolff algorithms. Field-mixing and multidimensional histogram techniques were employed in order to compute the probability distribution function of the extensive conjugate variables of interest and, using finite-size scaling analysis, the first-order transition line of the model was precisely located. The fourth-order cumulant of the order parameter was then calculated along this line and the bicritical point located with good precision from the cumulant crossings. The bicritical properties of this point were further investigated through the measurement of the universal probability distribution function of the order parameter. The results lead us to conclude that the studied bicritical point belongs in fact to the three-dimensional Heisenberg universality class.
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Affiliation(s)
- R T S Freire
- Universidade Federal de São João del Rei, Campus Dom Bosco, Praça Dom Helvécio, 74-Fábricas 36301-160, São João del Rei, MG-Brazil
| | - J A Plascak
- Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, C.P. 702, 30123-970, Belo Horizonte, MG-Brazil.,Universidade Federal da Paraíba, Centro de Ciências Exatas e da Natureza-Campus I, Departamento de Física-CCEN Cidade Universitária 58051-970, João Pessoa, PB-Brazil.,Center for Simulational Physics, University of Georgia, Athens, Georgia 30602, USA
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10
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Carvalho DC, Plascak JA, Castro LM. Quantum spin-1 anisotropic ferromagnetic Heisenberg model in a crystal field: a variational approach. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:032111. [PMID: 24125218 DOI: 10.1103/physreve.88.032111] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/27/2013] [Indexed: 06/02/2023]
Abstract
A variational approach based on Bogoliubov inequality for the free energy is employed in order to treat the quantum spin-1 anisotropic ferromagnetic Heisenberg model in the presence of a crystal field. Within the Bogoliubov scheme an improved pair approximation has been used. The temperature-dependent thermodynamic functions have been obtained and provide much better results than the previous simple mean-field scheme. In one dimension, which is still nonintegrable for quantum spin-1, we get the exact results in the classical limit, or near-exact results in the quantum case, for the free energy, magnetization, and quadrupole moment, as well for the transition temperature. In two and three dimensions the corresponding global phase diagrams have been obtained as a function of the parameters of the Hamiltonian. First-order transition lines, second-order transition lines, tricritical and tetracritical points, and critical endpoints have been located through the analysis of the minimum of the Helmholtz free energy and a Landau-like expansion in the approximated free energy. Only first-order quantum transitions have been found at zero temperature. Limiting cases, such as isotropic Heisenberg, Blume-Capel, and Ising models, have been analyzed and compared to previous results obtained from other analytical approaches as well as from Monte Carlo simulations.
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Affiliation(s)
- D C Carvalho
- Departamento de Física, Instituto de Ciências Exatas, Universidade Federal de Minas Gerais, Caixa Postale 702, 30123-970 Belo Horizonte, Minas Gerais, Brazil
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11
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Martins PHL. Probability distribution of the order parameter in the directed percolation universality class. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2012; 85:041110. [PMID: 22680423 DOI: 10.1103/physreve.85.041110] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/30/2011] [Indexed: 06/01/2023]
Abstract
The probability distributions of the order parameter for two models in the directed percolation universality class were evaluated. Monte Carlo simulations have been performed for the one-dimensional generalized contact process and the Domany-Kinzel cellular automaton. In both cases, the density of active sites was chosen as the order parameter. The criticality of those models was obtained by solely using the corresponding probability distribution function. It has been shown that the present method, which has been successfully employed in treating equilibrium systems, is indeed also useful in the study of nonequilibrium phase transitions.
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Affiliation(s)
- P H L Martins
- Instituto de Física, Universidade Federal de Mato Grosso, Av. Fernando Corrêa da Costa, 2367, Cuiabá, Mato Grosso, 78060-900, Brazil.
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12
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dos Anjos RA, Viana JR, de Sousa JR, Plascak JA. Three-dimensional Ising model with nearest- and next-nearest-neighbor interactions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:022103. [PMID: 17930090 DOI: 10.1103/physreve.76.022103] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/26/2007] [Indexed: 05/25/2023]
Abstract
The phase diagram of the Ising model in the presence of nearest- and next-nearest-neighbor interactions on a simple cubic lattice is studied within the framework of the differential operator technique. The Hamiltonian is solved by employing an effective-field theory with finite clusters consisting of a pair of spins. A functional form is also proposed for the free energy, similar to the Landau expansion, in order to obtain the phase diagram of the model. The transition from the ferromagnetic (or antiferromagnetic) phase to the disordered paramagnetic phase is of second order. On the other hand, a first-order transition is obtained from the lamellar phase to the paramagnetic phase, as well as from the lamellar phase to the ferromagnetic (or antiferromagnetic) phase, with the presence of a critical end point. An expected singular behavior of the first-order line at the critical end point is also obtained.
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Affiliation(s)
- Rosana A dos Anjos
- Departamento de Física, Universidade Federal do Amazonas, 3000 Japiim, 69077-000, Manaus-AM, Brazil
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13
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Martins PHL, Plascak JA. Universality class of the two-dimensional site-diluted Ising model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 76:012102. [PMID: 17677515 DOI: 10.1103/physreve.76.012102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/18/2007] [Indexed: 05/16/2023]
Abstract
In this work, we evaluate the probability distribution function of the order parameter for the two-dimensional site-diluted Ising model. Extensive Monte Carlo simulations have been performed for different spin concentrations p (0.70<or=p<or=1) on square lattices with linear sizes L (20<or=L<or=100). The results indicate that the universality class of the diluted Ising model seems to be independent of the amount of dilution. Logarithmic corrections of the finite-size critical temperature behavior of the model can also be inferred even for such small lattices.
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Affiliation(s)
- P H L Martins
- Núcleo de Física, Universidade Federal do Tocantins, Bloco II, 77020-210, Palmas, TO, Brazil
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14
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Tsai SH, Wang F, Landau DP. Critical endpoint behavior in an asymmetric Ising model: application of Wang-Landau sampling to calculate the density of states. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2007; 75:061108. [PMID: 17677221 DOI: 10.1103/physreve.75.061108] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/29/2007] [Indexed: 05/16/2023]
Abstract
Using the Wang-Landau sampling method with a two-dimensional random walk we determine the density of states for an asymmetric Ising model with two- and three-body interactions on a triangular lattice, in the presence of an external field. With an accurate density of states we were able to map out the phase diagram accurately and perform quantitative finite-size analyses at, and away from, the critical endpoint. We observe a clear divergence of the curvature of the spectator phase boundary and of the magnetization coexistence diameter derivative at the critical endpoint, and the exponents for both divergences agree well with previous theoretical predictions.
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Affiliation(s)
- Shan-Ho Tsai
- Center for Simulational Physics, University of Georgia, Athens, Georgia 30602, USA
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15
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Keskin M, Canko O, Deviren B. Dynamic phase transition in the kinetic spin- Blume-Capel model under a time-dependent oscillating external field. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2006; 74:011110. [PMID: 16907063 DOI: 10.1103/physreve.74.011110] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/06/2006] [Indexed: 05/11/2023]
Abstract
We present a study, within a mean-field approach, of the stationary states of the kinetic spin-3/2 Blume-Capel model in the presence of a time-dependent oscillating external magnetic field. We use the Glauber-type stochastic dynamics to describe the time evolution of the system. We have found that the behavior of the system strongly depends on the crystal-field interaction. We can identify two types of solutions: a symmetric one where the magnetization (m) of the system oscillates in time around zero, which corresponds to a paramagnetic phase (P), and an antisymmetric one where m oscillates in time around a finite value different from zero, namely +/-3/2 and +/-1/2 that corresponds to the ferromagnetic-3/2 (F3/2) and the ferromagnetic-1/2 (F1/2) phases, respectively. There are coexistence regions of the phase space where the F3/2, F1/2, (F3/2 + F1/2), F3/2, P(F3/2 + P), F1/2, and P(F1/2 + P), F3/2, F1/2, P(F3/2 + F1/2 + P) phases coexist, hence the system exhibits seven different phases. We obtain the dynamic phase transition points and find six fundamental phase diagrams which exhibit one or three dynamic tricritical points. We have also calculated the Liapunov exponent to verify the stability of the solutions and the dynamic phase transition points.
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Affiliation(s)
- Mustafa Keskin
- Department of Physics, Erciyes University, 38039 Kayseri, Turkey
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16
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Freire RTS, Mitchell SJ, Plascak JA, Landau DP. Monte Carlo study of the vector Blume-Emery-Griffiths model for 3He--4He mixtures in three dimensions. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:056117. [PMID: 16383698 DOI: 10.1103/physreve.72.056117] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2005] [Indexed: 05/05/2023]
Abstract
A version of the Vector Blume-Emery-Griffiths model with three-dimensional spins was studied on a simple cubic lattice by Monte Carlo simulations. We obtained the phase diagram, which reproduces, for a range of the parameters of the model, the topology of the one observed for bulk mixtures of 3He--4He. The phase diagram displays a superfluid, 4He-rich phase which undergoes a phase transition to a normal phase. This transition is first or second order, depending on the region of the phase diagram examined. One of the main features of this diagram is the existence of a tricritical point, which, for some values of the parameters of the model, decomposes into a critical endpoint and a double critical endpoint. These points were located with reasonable precision. This study provides the basis for the subsequent study of dynamic properties of 3He--4He mixtures.
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Affiliation(s)
- R T S Freire
- Center for Simulational Physics, University of Georgia, Athens, GA 30602, USA.
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17
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Grandi BCS, Figueiredo W. Short-time dynamics for the spin-3/2 Blume-Capel model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2004; 70:056109. [PMID: 15600694 DOI: 10.1103/physreve.70.056109] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/30/2004] [Indexed: 05/24/2023]
Abstract
We employed Monte Carlo simulations and short-time dynamic scaling to determine the static and dynamic critical exponents for the generalized two-dimensional Blume-Capel model of spin-3/2. We showed that the critical behavior at the second-order phase-transition line between the paramagnetic and ferromagnetic phases is in the same universality class of the two-dimensional Ising model. However, at the double critical end point, which is present in the phase diagram of the model, the critical exponent beta , associated to the order parameter, is different from that of the Ising model.
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Affiliation(s)
- B C S Grandi
- Departamento de Física, Universidade Federal de Santa Catarina, 88040-900 Florianópolis, SC, Brazil
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