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Münster L, Norrenbrock C, Hartmann AK, Young AP. Ordering behavior of the two-dimensional Ising spin glass with long-range correlated disorder. Phys Rev E 2021; 103:042117. [PMID: 34005869 DOI: 10.1103/physreve.103.042117] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/01/2021] [Accepted: 03/22/2021] [Indexed: 11/07/2022]
Abstract
The standard short-range two-dimensional Ising spin glass is numerically well accessible, in particular, because there are polynomial-time ground-state algorithms. On the other hand, in contrast to higher dimensional spin glasses, it does not exhibit a rich behavior, i.e., no ordered phase at finite temperature. Here, we investigate whether long-range correlated bonds change this behavior. This would still keep the model numerically well accessible while exhibiting a more interesting behavior. The bonds are drawn from a Gaussian distribution with a two-point correlation for bonds at distance r that decays as (1+r^{2})^{-a/2}, a≥0. We study numerically with exact algorithms the ground-state and domain-wall excitations. Our results indicate that the inclusion of bond correlations still does not lead to a spin-glass order at any finite temperature. A further analysis reveals that bond correlations have a strong effect at local length scales, inducing ferro- and antiferromagnetic domains into the system. The length scale of ferro- and antiferromagnetic order diverges exponentially as the correlation exponent approaches a critical value, a→a_{crit}=0. Thus, our results suggest that the system becomes a ferro- or antiferromagnet only in the limit a→0.
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Affiliation(s)
- L Münster
- Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany
| | - C Norrenbrock
- Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany
| | - A K Hartmann
- Institut für Physik, Universität Oldenburg, 26111 Oldenburg, Germany
| | - A P Young
- University of California Santa Cruz, California 95064, USA
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2
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Makarova K, Strongin V, Titovets I, Syrov A, Zinchenko I, Samoylov V, Hofhuis K, Saccone M, Makarov A, Farhan A, Nefedev K. Low-energy states, ground states, and variable frustrations of the finite-size dipolar Cairo lattices. Phys Rev E 2021; 103:042129. [PMID: 34005950 DOI: 10.1103/physreve.103.042129] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/09/2020] [Accepted: 03/16/2021] [Indexed: 11/07/2022]
Abstract
To investigate the influence of geometric frustration on the properties of low-energy configurations of systems of ferromagnetic nanoislands located on the edges of the Cairo lattice, the model of interacting Ising-like magnetic dipoles is used. By the method of complete enumeration, the densities of states of the Cairo pentagonal lattices of a finite number of Ising-like point dipoles are calculated. The calculated ground and low-energy states for systems with a small number of dipoles can be used to solve the problem of searching for the ground states in a system with a relatively large number of dipoles. It is shown that the ground-state energy of the Cairo pentagonal lattices exhibits nonmonotonic behavior on one of the lattice parameters. The lattice parameters can be used to control the degree of geometric frustration. For the studied lattices of a finite number of Ising dipoles on the Cairo lattice in the ground-state configurations, a number of closed pentagons is observed, which are different from the obtained maximum closed pentagons. The magnetic order in the ground-state configurations obeys the ice rule and the quasi-ice rules.
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Affiliation(s)
- Kseniia Makarova
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, Russky Island, 10 Ajax Bay, 690922, Russian Federation.,Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok, Radio 7, 690041, Russian Federation
| | - Vladislav Strongin
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, Russky Island, 10 Ajax Bay, 690922, Russian Federation.,Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok, Radio 7, 690041, Russian Federation
| | - Iuliia Titovets
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, Russky Island, 10 Ajax Bay, 690922, Russian Federation
| | - Aleksandr Syrov
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, Russky Island, 10 Ajax Bay, 690922, Russian Federation
| | - Ivan Zinchenko
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, Russky Island, 10 Ajax Bay, 690922, Russian Federation.,Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok, Radio 7, 690041, Russian Federation
| | - Victor Samoylov
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, Russky Island, 10 Ajax Bay, 690922, Russian Federation.,Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok, Radio 7, 690041, Russian Federation
| | - Kevin Hofhuis
- Laboratory for Mesoscopic Systems, Department of Materials, ETH Zurich, CH-8093 Zurich, Switzerland.,Laboratory for Multiscale Materials Experiments, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland
| | - Michael Saccone
- Physics Department, University of California, 1156 High Street, Santa Cruz, California 95064, USA
| | - Aleksandr Makarov
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, Russky Island, 10 Ajax Bay, 690922, Russian Federation.,Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok, Radio 7, 690041, Russian Federation
| | - Alan Farhan
- Laboratory for Multiscale Materials Experiments, Paul Scherrer Institute, CH-5232 Villigen PSI, Switzerland.,Department of Applied Physics, Aalto University School of Science, P.O. Box 15100, FI-00076 Aalto, Finland
| | - Konstantin Nefedev
- School of Natural Sciences, Far Eastern Federal University, Vladivostok, Russky Island, 10 Ajax Bay, 690922, Russian Federation.,Institute of Applied Mathematics, Far Eastern Branch, Russian Academy of Science, Vladivostok, Radio 7, 690041, Russian Federation
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Rocchi J, Saad D, Yeung CH. Slow spin dynamics and self-sustained clusters in sparsely connected systems. Phys Rev E 2018; 97:062154. [PMID: 30011498 DOI: 10.1103/physreve.97.062154] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2017] [Indexed: 11/07/2022]
Abstract
To identify emerging microscopic structures in low-temperature spin glasses, we study self-sustained clusters (SSC) in spin models defined on sparse random graphs. A message-passing algorithm is developed to determine the probability of individual spins to belong to SSC. We then compare the predicted SSC associations with the dynamical properties of spins obtained from numerical simulations and show that SSC association identifies individual slow-evolving spins. Studies of Erdos-Renyi (ER) and random regular (RR) graphs show that spins belonging to SSC are more stable with respect to spin-flip fluctuations, as suggested by the analysis of fully connected models. Further analyses show that SSC association outperforms local fields in predicting the spin dynamics, specifically the group of slow- and fast-evolving spins in RR graphs, for a wide temperature range close to the spin-glass transition. This insight gives rise to a powerful approach for predicting individual spin dynamics from a single snapshot of an equilibrium spin configuration, namely from limited static information. It also implies that single-sample SSC association carries more information than local fields in describing the state of individual spins, when little information can be extracted from the system's topology.
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Affiliation(s)
- Jacopo Rocchi
- Nonlinearity and Complexity Research Group, Aston University, Birmingham B4 7ET, United Kingdom
| | - David Saad
- Nonlinearity and Complexity Research Group, Aston University, Birmingham B4 7ET, United Kingdom
| | - Chi Ho Yeung
- Department of Science and Environmental Studies, The Education University of Hong Kong, Hong Kong
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Romá F, Risau-Gusman S. Backbone structure of the Edwards-Anderson spin-glass model. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2013; 88:042105. [PMID: 24229114 DOI: 10.1103/physreve.88.042105] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/05/2013] [Indexed: 06/02/2023]
Abstract
We study the ground-state spatial heterogeneities of the Edwards-Anderson spin-glass model with both bimodal and Gaussian bond distributions. We characterize these heterogeneities by using a general definition of bond rigidity, which allows us to classify the bonds of the system into two sets, the backbone and its complement, with very different properties. This generalizes to continuous distributions of bonds the well-known definition of a backbone for discrete bond distributions. By extensive numerical simulations we find that the topological structure of the backbone for a given lattice dimensionality is very similar for both discrete and continuous bond distributions. We then analyze how these heterogeneities influence the equilibrium properties at finite temperature and we discuss the possibility that a suitable backbone picture can be relevant to describe spin-glass phenomena.
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Affiliation(s)
- F Romá
- Departamento de Física, INFAP, CONICET, Universidad Nacional de San Luis, Chacabuco 917, D5700BWS San Luis, Argentina
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Poulin D, Wocjan P. Preparing ground States of quantum many-body systems on a quantum computer. PHYSICAL REVIEW LETTERS 2009; 102:130503. [PMID: 19392338 DOI: 10.1103/physrevlett.102.130503] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 09/17/2008] [Indexed: 05/27/2023]
Abstract
Preparing the ground state of a system of interacting classical particles is an NP-hard problem. Thus, there is in general no better algorithm to solve this problem than exhaustively going through all N configurations of the system to determine the one with lowest energy, requiring a running time proportional to N. A quantum computer, if it could be built, could solve this problem in time sqrt[N]. Here, we present a powerful extension of this result to the case of interacting quantum particles, demonstrating that a quantum computer can prepare the ground state of a quantum system as efficiently as it does for classical systems.
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Affiliation(s)
- David Poulin
- Département de Physique, Université de Sherbrooke, Sherbrooke, Québec, Canada.
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Pardella G, Liers F. Exact ground states of large two-dimensional planar Ising spin glasses. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 78:056705. [PMID: 19113235 DOI: 10.1103/physreve.78.056705] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/21/2008] [Revised: 10/06/2008] [Indexed: 05/27/2023]
Abstract
Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed to a minimum-weight perfect matching problem, the reachable system sizes have been limited both by the needed CPU time and by memory requirements. In this work, we present an algorithm for the calculation of exact ground states for two-dimensional Ising spin glasses with free boundary conditions in at least one direction. The algorithmic foundations of the method date back to the work of Kasteleyn from the 1960s for computing the complete partition function of the Ising model. Using Kasteleyn cities, we calculate exact ground states for huge two-dimensional planar Ising spin-glass lattices (up to 3000;{2} spins) within reasonable time. According to our knowledge, these are the largest sizes currently available. Kasteleyn cities were recently also used by Thomas and Middleton in the context of extended ground states on the torus. Moreover, they show that the method can also be used for computing ground states of planar graphs. Furthermore, we point out that the correctness of heuristically computed ground states can easily be verified. Finally, we evaluate the solution quality of heuristic variants of the L. Bieche approach.
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Affiliation(s)
- G Pardella
- Institut für Informatik, Universität zu Köln, Pohligstrasse 1, D-50969 Köln, Germany.
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Hastings MB. Inference from matrix products: a heuristic spin-glass algorithm. PHYSICAL REVIEW LETTERS 2008; 101:167206. [PMID: 18999711 DOI: 10.1103/physrevlett.101.167206] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/21/2008] [Indexed: 05/27/2023]
Abstract
We present an algorithm for finding ground states of two-dimensional spin-glass systems based on ideas from matrix product states in quantum information theory. The algorithm works directly at zero temperature and defines an approximation to the energy whose accuracy depends on a parameter k. We test the algorithm against exact methods on random field and random bond Ising models, and we find that accurate results require a k which scales roughly polynomially with the system size. The algorithm also performs well when tested on small systems with arbitrary interactions, where no fast, exact algorithms exist. The time required is significantly less than Monte Carlo schemes.
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Affiliation(s)
- M B Hastings
- Center for Nonlinear Studies and Theoretical Division, Los Alamos National Laboratory, Los Alamos, NM 87545, USA
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Romá F, Bustingorry S, Gleiser PM, Domínguez D. Strong dynamical heterogeneities in the violation of the fluctuation-dissipation theorem in spin glasses. PHYSICAL REVIEW LETTERS 2007; 98:097203. [PMID: 17359192 DOI: 10.1103/physrevlett.98.097203] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/28/2006] [Revised: 11/09/2006] [Indexed: 05/14/2023]
Abstract
We analyze numerically the violation of the fluctuation-dissipation theorem (FDT) in the +/-J Edwards-Anderson (EA) spin-glass model. Using single spin probability densities we reveal the presence of strong dynamical heterogeneities, which correlate with ground-state information. The physical interpretation of the results shows that the spins can be divided into two sets. In 3D, one set forms a compact structure which presents a coarseninglike behavior with its characteristic violation of the FDT, while the other asymptotically follows the FDT. Finally, we compare the dynamical behavior observed in 3D with 2D.
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Affiliation(s)
- F Romá
- Centro Atómico Bariloche, 8400 San Carlos de Bariloche, Río Negro, Argentina
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9
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Calculating exact ground states of spin glasses: A polyhedral approach. ACTA ACUST UNITED AC 2006. [DOI: 10.1007/bfb0057526] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register]
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10
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Romá F, Bustingorry S, Gleiser PM. Signature of the ground-state topology in the low-temperature dynamics of spin glasses. PHYSICAL REVIEW LETTERS 2006; 96:167205. [PMID: 16712269 DOI: 10.1103/physrevlett.96.167205] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/07/2005] [Indexed: 05/09/2023]
Abstract
We numerically address the issue of how the ground-state topology is reflected in the finite temperature dynamics of the +/-J Edwards-Anderson spin glass model. In this system a careful study of the ground-state configurations allows us to classify spins into two sets: solidary and nonsolidary spins. We show that these sets quantitatively account for the dynamical heterogeneities found in the mean flipping time distribution at finite low temperatures. The results highlight the relevance of taking into account the ground-state topology in the analysis of the finite temperature dynamics of spin glasses.
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Affiliation(s)
- F Romá
- Centro Atómico Bariloche, Consejo Nacional de Investigaciones Científicas y Técnicas, 8400 San Carlos de Bariloche, Río Negro, Argentina
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11
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Bauer M, Orland H. Checking for optimal solutions in some NP-complete problems. PHYSICAL REVIEW LETTERS 2005; 95:107202. [PMID: 16196960 DOI: 10.1103/physrevlett.95.107202] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/01/2005] [Indexed: 05/04/2023]
Abstract
For some weighted NP-complete problems, checking whether a proposed solution is optimal is a nontrivial task. Such is the case for the traveling salesman problem, or the spin-glass problem in three dimensions. In this Letter, we consider the weighted tripartite matching problem, a well known NP-complete problem. We write mean-field finite temperature equations for this model and derive their zero temperature limit. We show that any solution of the zero temperature equations provides an exact absolute ground state of the system. As a consequence, we propose a criterion which can be checked in polynomial time, and such that given a putative optimal solution, if the criterion is satisfied, then the solution is indeed optimal. This criterion is generalized to a class of variants of the multiple traveling salesmen problems.
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Affiliation(s)
- Michel Bauer
- Service de Physique Théorique, CEA-Saclay, Gif-sur-Yvette, France
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Wang JS. Worm algorithm for two-dimensional spin glasses. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2005; 72:036706. [PMID: 16241613 DOI: 10.1103/physreve.72.036706] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/10/2005] [Indexed: 05/05/2023]
Abstract
A worm algorithm is proposed for the two-dimensional spin glasses. The method is based on a low-temperature expansion of the partition function. The low-temperature configurations of the spin glass on square lattice can be viewed as strings connecting pairs of frustrated plaquettes. The worm algorithm directly manipulates these strings. It is shown that the worm algorithm is efficient, particularly if free boundary conditions are used. We obtain accurate low-temperature specific heat data consistent with a form c approximately T-2 exp [-2J/( kB T) ] , where T is temperature and J is coupling constant, for the two-dimensional +/- J spin glass.
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Affiliation(s)
- Jian-Sheng Wang
- Singapore-MIT Alliance and Department of Computational Science, National University of Singapore, Singapore 117543, Republic of Singapore
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Hed G, Hartmann AK, Stauffer D, Domany E. Spin domains generate hierarchical ground state structure in J = +/-1 spin glasses. PHYSICAL REVIEW LETTERS 2001; 86:3148-3151. [PMID: 11290129 DOI: 10.1103/physrevlett.86.3148] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/24/2000] [Indexed: 05/23/2023]
Abstract
Unbiased samples of ground states were generated for the short-range Ising spin glass with J(ij) = +/-1, in three dimensions. Clustering the ground states revealed their hierarchical structure, which is explained by correlated spin domains, serving as cores for macroscopic zero energy "excitations."
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Affiliation(s)
- G Hed
- Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot, Israel
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Curado EM, Nobre FD, Coutinho S. Ground-state degeneracies of Ising spin glasses on diamond hierarchical lattices. PHYSICAL REVIEW. E, STATISTICAL PHYSICS, PLASMAS, FLUIDS, AND RELATED INTERDISCIPLINARY TOPICS 1999; 60:3761-70. [PMID: 11970209 DOI: 10.1103/physreve.60.3761] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/21/1998] [Revised: 05/10/1999] [Indexed: 11/07/2022]
Abstract
The total number of ground states for short-range Ising spin glasses, defined on diamond hierarchical lattices of fractal dimensions d=2, 3, 4, 5, and 2.58, is estimated by means of analytic calculations (three last hierarchy levels of the d=2 lattice) and numerical simulations (lower hierarchies for d=2 and all remaining cases). It is shown that in the case of continuous probability distributions for the couplings, the number of ground states is finite in the thermodynamic limit. However, for a bimodal probability distribution (+/-J with probabilities p and 1-p, respectively), the average number of ground states is maximum for a wide range of values of p around p=1 / 2 and depends on the total number of sites at hierarchy level n, Nn. In this case, for all lattices investigated, it is shown that the ground-state degeneracy behaves like exp[h(d)Nn], in the limit Nn large, where h(d) is a positive number which depends on the lattice fractal dimension. The probability of finding frustrated cells at a given hierarchy level n, Fn(p), is calculated analytically (three last hierarchy levels for d=2 and the last hierarchy of the d=3 lattice, with 0<or=p<or=1), as well as numerically (all other cases, with p=1 / 2). Except for d=2, in which case Fn(1 / 2) increases by decreasing the hierarchy level, all other dimensions investigated present an exponential decrease in Fn(1 / 2) for decreasing values of n. For d=2 our results refer to the paramagnetic phase, whereas for all other dimensions considered [which are greater than the lower critical dimension dl (dl approximately 2.5)], our results refer to the spin-glass phase at zero temperature; in the latter cases h(d) increases with the fractal dimension. For n>>1, only the last hierarchies contribute significantly to the ground-state degeneracy; such a dominant behavior becomes stronger for high fractal dimensions. The exponential increase of the number of ground states with the total number of sites is in agreement with the mean-field picture of spin glasses.
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Affiliation(s)
- E M Curado
- Centro Brasiliro de Pesquisas Físicas, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, RJ, Brazil
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Barahona F, Maccioni E. On the exact ground states of three-dimensional Ising spin glasses. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/15/11/008] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Kawashima N, Suzuki M. Replica optimization method for ground-state search of random spin systems. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/25/5/014] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Klotz T, Kobe S. "Valley structures" in the phase space of a finite 3D Ising spin glass with +or-I interactions. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/27/4/001] [Citation(s) in RCA: 48] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022]
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Wille LT, Vennik J. Computational complexity of the ground-state determination of atomic clusters. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/18/8/003] [Citation(s) in RCA: 151] [Impact Index Per Article: 6.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Freund H, Grassberger P. The ground state of the +or-J spin glass from a heuristic matching algorithm. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/22/18/036] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Barahona F. Ground-state magnetization of Ising spin glasses. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:12864-12867. [PMID: 10010194 DOI: 10.1103/physrevb.49.12864] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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Vogel EE, Cartes J, Contreras S, Lebrecht W, Villegas J. Ground-state properties of finite square and triangular Ising lattices with mixed exchange interactions. PHYSICAL REVIEW. B, CONDENSED MATTER 1994; 49:6018-6027. [PMID: 10011581 DOI: 10.1103/physrevb.49.6018] [Citation(s) in RCA: 22] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
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Abstract
It is believed that the native folded three-dimensional conformation of a protein is its lowest free energy state, or one of its lowest. It is shown here that both a two- and three-dimensional mathematical model describing the folding process as a free energy minimization problem is NP-hard. This means that the problem belongs to a large set of computational problems, assumed to be very hard ("conditionally intractable"). Some of the possible ramifications of this result are speculated upon.
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Affiliation(s)
- A S Fraenkel
- Department of Mathematics, University of Pennsylvania, Philadelphia 19104-6395
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Stolorz P. Recursive approaches to the analysis of short-range disorded systems in the low-temperature regime. PHYSICAL REVIEW. B, CONDENSED MATTER 1993; 48:3085-3089. [PMID: 10008729 DOI: 10.1103/physrevb.48.3085] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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30
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Blackman JA, Poulter J. Gauge-invariant method for the +/-J spin-glass model. PHYSICAL REVIEW. B, CONDENSED MATTER 1991; 44:4374-4386. [PMID: 10000087 DOI: 10.1103/physrevb.44.4374] [Citation(s) in RCA: 19] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 04/12/2023]
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