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Corberi F, Smaldone L. Ordering kinetics of the two-dimensional voter model with long-range interactions. Phys Rev E 2024; 109:034133. [PMID: 38632821 DOI: 10.1103/physreve.109.034133] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/01/2023] [Accepted: 03/04/2024] [Indexed: 04/19/2024]
Abstract
We study analytically the ordering kinetics of the two-dimensional long-range voter model on a two-dimensional lattice, where agents on each vertex take the opinion of others at distance r with probability P(r)∝r^{-α}. The model is characterized by different regimes, as α is varied. For α>4, the behavior is similar to that of the nearest-neighbor model, with the formation of ordered domains of a typical size growing as L(t)∝sqrt[t], until consensus is reached in a time of the order of NlnN, with N being the number of agents. Dynamical scaling is violated due to an excess of interfacial sites whose density decays as slowly as ρ(t)∝1/lnt. Sizable finite-time corrections are also present, which are absent in the case of nearest-neighbor interactions. For 0<α≤4, standard scaling is reinstated and the correlation length increases algebraically as L(t)∝t^{1/z}, with 1/z=2/α for 3<α<4 and 1/z=2/3 for 0<α<3. In addition, for α≤3, L(t) depends on N at any time t>0. Such coarsening, however, only leads the system to a partially ordered metastable state where correlations decay algebraically with distance, and whose lifetime diverges in the N→∞ limit. In finite systems, consensus is reached in a time of the order of N for any α<4.
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Affiliation(s)
- Federico Corberi
- Dipartimento di Fisica, Università di Salerno, Via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy and INFN Sezione di Napoli, Gruppo Collegato di Salerno, Italy
| | - Luca Smaldone
- Dipartimento di Fisica, Università di Salerno, Via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy and INFN Sezione di Napoli, Gruppo Collegato di Salerno, Italy
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Bhandari P, Malik V, Puri S. Phase-ordering kinetics of the asymmetric Coulomb glass model. Phys Rev E 2024; 109:014135. [PMID: 38366509 DOI: 10.1103/physreve.109.014135] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/21/2023] [Accepted: 01/03/2024] [Indexed: 02/18/2024]
Abstract
We present results for phase-ordering kinetics in the Coulomb glass (CG) model, which describes electrons on a lattice with unscreened Coulombic repulsion. The filling factor is denoted by K∈[0,1]. For a square lattice with K=0.5 (symmetric CG), the ground state is a checkerboard with alternating electrons and holes. In this paper, we focus on the asymmetric CG where K≲0.5, i.e., the ground state is checkerboard-like with excess holes distributed uniformly. There is no explicit quenched disorder in our system, though the Coulombic interaction gives rise to frustration. We find that the evolution morphology is in the same dynamical universality class as the ordering ferromagnet. Further, the domain growth law is slightly slower than the Lifshitz-Cahn-Allen law, L(t)∼t^{1/2}, i.e., the growth exponent is underestimated. We speculate that this could be a signature of logarithmic growth in the asymptotic regime.
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Affiliation(s)
- Preeti Bhandari
- Department of Physics, Ben Gurion University of the Negev, Beer Sheva 84105, Israel
| | - Vikas Malik
- Department of Physics and Material Science, Jaypee Institute of Information Technology, Uttar Pradesh 201309, India
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi-110067, India
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Agrawal R, Cugliandolo LF, Faoro L, Ioffe LB, Picco M. Nonequilibrium critical dynamics of the two-dimensional ±J Ising model. Phys Rev E 2023; 108:064131. [PMID: 38243541 DOI: 10.1103/physreve.108.064131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/13/2023] [Accepted: 10/19/2023] [Indexed: 01/21/2024]
Abstract
The ±J Ising model is a simple frustrated spin model, where the exchange couplings independently take the discrete value -J with probability p and +J with probability 1-p. It is especially appealing due to its connection to quantum error correcting codes. Here, we investigate the nonequilibrium critical behavior of the two-dimensional ±J Ising model, after a quench from different initial conditions to a critical point T_{c}(p) on the paramagnetic-ferromagnetic (PF) transition line, especially above, below, and at the multicritical Nishimori point (NP). The dynamical critical exponent z_{c} seems to exhibit nonuniversal behavior for quenches above and below the NP, which is identified as a preasymptotic feature due to the repulsive fixed point at the NP, whereas for a quench directly to the NP, the dynamics reaches the asymptotic regime with z_{c}≃6.02(6). We also consider the geometrical spin clusters (of like spin signs) during the critical dynamics. Each universality class on the PF line is uniquely characterized by the stochastic Loewner evolution with corresponding parameter κ. Moreover, for the critical quenches from the paramagnetic phase, the model, irrespective of the frustration, exhibits an emergent critical percolation topology at the large length scales.
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Affiliation(s)
- Ramgopal Agrawal
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Leticia F Cugliandolo
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
- Institut Universitaire de France, 1 rue Descartes, 75231 Paris Cedex 05, France
| | - Lara Faoro
- Google Research, Mountain View, California 94043, USA
| | - Lev B Ioffe
- Google Research, Mountain View, California 94043, USA
| | - Marco Picco
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
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Agrawal R, Corberi F, Lippiello E, Puri S. Phase ordering dynamics of the random-field long-range Ising model in one dimension. Phys Rev E 2023; 108:044131. [PMID: 37978597 DOI: 10.1103/physreve.108.044131] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/11/2023] [Accepted: 08/28/2023] [Indexed: 11/19/2023]
Abstract
We investigate the influence of long-range (LR) interactions on the phase ordering dynamics of the one-dimensional random-field Ising model (RFIM). Unlike the usual RFIM, a spin interacts with all other spins through a ferromagnetic coupling that decays as r^{-(1+σ)}, where r is the distance between two spins. In the absence of LR interactions, the size of coarsening domains R(t) exhibits a crossover from pure system behavior R(t)∼t^{1/2} to an asymptotic regime characterized by logarithmic growth: R(t)∼(lnt)^{2}. The LR interactions affect the preasymptotic regime, which now exhibits ballistic growth R(t)∼t, followed by σ-dependent growth R(t)∼t^{1/(1+σ)}. Additionally, the LR interactions also affect the asymptotic logarithmic growth, which becomes R(t)∼(lnt)^{α(σ)} with α(σ)<2. Thus, LR interactions lead to faster growth than for the nearest-neighbor system at short times. Unexpectedly, this driving force causes a slowing down of the dynamics (α<2) in the asymptotic logarithmic regime. This is explained in terms of a nontrivial competition between the pinning force caused by the random field and the driving force introduced by LR interactions. We also study the spatial correlation function and the autocorrelation function of the magnetization field. The former exhibits superuniversality for all σ, i.e., a scaling function that is independent of the disorder strength. The same holds for the autocorrelation function when σ<1, whereas a signature of the violation of superuniversality is seen for σ>1.
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Affiliation(s)
- Ramgopal Agrawal
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
- Sorbonne Université, Laboratoire de Physique Théorique et Hautes Energies, CNRS UMR 7589, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - Federico Corberi
- Dipartimento di Fisica "E. R. Caianiello", and INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
| | - Eugenio Lippiello
- Dipartimento di Matematica e Fisica, Università della Campania, Viale Lincoln 5, 81100, Caserta, Italy
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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Müller F, Christiansen H, Janke W. Phase-Separation Kinetics in the Two-Dimensional Long-Range Ising Model. PHYSICAL REVIEW LETTERS 2022; 129:240601. [PMID: 36563254 DOI: 10.1103/physrevlett.129.240601] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/18/2022] [Accepted: 11/08/2022] [Indexed: 06/17/2023]
Abstract
Using Monte Carlo computer simulations, we investigate the kinetics of phase separation in the two-dimensional conserved Ising model with power-law decaying long-range interactions, the prototypical model for many long-range interacting systems. A long-standing analytical prediction for the characteristic length is shown to be applicable. In the simulation, we relied on our novel algorithm which provides a massive speedup for long-range interacting systems.
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Affiliation(s)
- Fabio Müller
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
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Agrawal R, Corberi F, Insalata F, Puri S. Asymptotic states of Ising ferromagnets with long-range interactions. Phys Rev E 2022; 105:034131. [PMID: 35428063 DOI: 10.1103/physreve.105.034131] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/18/2021] [Accepted: 03/02/2022] [Indexed: 06/14/2023]
Abstract
It is known that, after a quench to zero temperature (T=0), two-dimensional (d=2) Ising ferromagnets with short-range interactions do not always relax to the ordered state. They can also fall in infinitely long-lived striped metastable states with a finite probability. In this paper, we study how the abundance of striped states is affected by long-range interactions. We investigate the relaxation of d=2 Ising ferromagnets with power-law interactions by means of Monte Carlo simulations at both T=0 and T≠0. For T=0 and the finite system size, the striped metastable states are suppressed by long-range interactions. In the thermodynamic limit, their occurrence probabilities are consistent with the short-range case. For T≠0, the final state is always ordered. Further, the equilibration occurs at earlier times with an increase in the strength of the interactions.
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Affiliation(s)
- Ramgopal Agrawal
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
| | - Federico Corberi
- Dipartimento di Fisica "E. R. Caianiello", and INFN, Gruppo Collegato di Salerno, and CNISM, Unità di Salerno, Università di Salerno, via Giovanni Paolo II 132, 84084 Fisciano (SA), Italy
| | - Ferdinando Insalata
- Department of Mathematics, Imperial College London, London SW7 2AZ, United Kingdom
| | - Sanjay Puri
- School of Physical Sciences, Jawaharlal Nehru University, New Delhi 110067, India
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Christiansen H, Majumder S, Janke W. Zero-temperature coarsening in the two-dimensional long-range Ising model. Phys Rev E 2021; 103:052122. [PMID: 34134321 DOI: 10.1103/physreve.103.052122] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/11/2020] [Accepted: 04/20/2021] [Indexed: 11/07/2022]
Abstract
We investigate the nonequilibrium dynamics following a quench to zero temperature of the nonconserved Ising model with power-law decaying long-range interactions ∝1/r^{d+σ} in d=2 spatial dimensions. The zero-temperature coarsening is always of special interest among nonequilibrium processes, because often peculiar behavior is observed. We provide estimates of the nonequilibrium exponents, viz., the growth exponent α, the persistence exponent θ, and the fractal dimension d_{f}. It is found that the growth exponent α≈3/4 is independent of σ and different from α=1/2, as expected for nearest-neighbor models. In the large σ regime of the tunable interactions only the fractal dimension d_{f} of the nearest-neighbor Ising model is recovered, while the other exponents differ significantly. For the persistence exponents θ this is a direct consequence of the different growth exponents α as can be understood from the relation d-d_{f}=θ/α; they just differ by the ratio of the growth exponents ≈3/2. This relation has been proposed for annihilation processes and later numerically tested for the d=2 nearest-neighbor Ising model. We confirm this relation for all σ studied, reinforcing its general validity.
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Affiliation(s)
- Henrik Christiansen
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Suman Majumder
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
| | - Wolfhard Janke
- Institut für Theoretische Physik, Universität Leipzig, IPF 231101, 04081 Leipzig, Germany
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