Approximate ground states of the random-field Potts model from graph cuts

Kumar, M. Pawan; Kumar, Ravinder; Weigel, Martin; Banerjee, Varsha; Janke, Wolfhard; Puri, Sanjay

doi:10.1103/physreve.97.053307

Cited by 11 publications

(19 citation statements)

References 72 publications

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“…In combination with our simple, parametric scheme for choosing the temperature schedule, the proposed simulation framework provides an accessible and highly performant code base for the simulation of spin-glass systems that can easily be extended to other systems with quenched disorder such as the random-field problem [75].…”

Section: Discussionmentioning

confidence: 99%

Massively parallel simulations for disordered systems

et al. 2020

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Simulations of systems with quenched disorder are extremely demanding, suffering from the combined effect of slow relaxation and the need of performing the disorder average. As a consequence, new algorithms and improved implementations in combination with alternative and even purpose-built hardware are often instrumental for conducting meaningful studies of such systems. The ensuing demands regarding hardware availability and code complexity are substantial and sometimes prohibitive. We demonstrate how with a moderate coding effort leaving the overall structure of the simulation code unaltered as compared to a CPU implementation, very significant speed-ups can be achieved from a parallel code on GPU by mainly exploiting the trivial parallelism of the disorder samples and the near-trivial parallelism of the parallel tempering replicas. A combination of this massively parallel implementation with a careful choice of the temperature protocol for parallel tempering as well as efficient cluster updates allows us to equilibrate comparatively large systems with moderate computational resources.

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Section: Discussionmentioning

confidence: 99%

Massively parallel simulations for disordered systems

et al. 2020

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“…In both cases, the resulting embedded binary (Ising type) problems are solved exactly using the established techniques for maximum-flow [12][13][14]. For our application to the RFPM we focus on the α-expansion move which we have shown previously to be quite efficient for finding approximate ground states of this system [18]. By construction, this approach is not guaranteed to result in a ground state, but it will normally lead to a metastable configuration.…”

Section: Model and Methodologymentioning

confidence: 99%

“…The approach is stochastic in that the final state depends on the chosen initial spin configuration. As a consequence, results can be systematically improved by performing n independent runs with random initial conditions and picking the result of lowest energy [18,22]. Since α-expansion cannot increase the energy, this approach is guaranteed to result in the exact answer if (but not only if) the ground state was among the initial configurations.…”

Section: Model and Methodologymentioning

confidence: 99%

“…To handle such systems, one might relax the demand of finding exact ground states and revert to stochastic approaches that provide approximate global minima with moderate effort. We have recently shown that this is possible for the case of the random-field Potts model (RFPM) with recourse to suitable generalizations of the graph-cut (GC) methods used for the RFIM [18]. This approach relies on techniques initially developed for problems in computer vision [17].…”

Section: Introductionmentioning

confidence: 99%

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On the comparison of optimization algorithms for the random-field Potts model

Kumar

Weigel

2022

J. Phys.: Conf. Ser.

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For many systems with quenched disorder the study of ground states can crucially contribute to a thorough understanding of the physics at play, be it for the critical behavior if that is governed by a zero-temperature fixed point or for uncovering properties of the ordered phase. While ground states can in principle be computed using general-purpose optimization algorithms such as simulated annealing or genetic algorithms, it is often much more efficient to use exact or approximate techniques specifically tailored to the problem at hand. For certain systems with discrete degrees of freedom such as the random-field Ising model, there are polynomial-time methods to compute exact ground states. But even as the number of states increases beyond two as in the random-field Potts model, the problem becomes NP hard and one cannot hope to find exact ground states for relevant system sizes. Here, we compare a number of approximate techniques for this problem and evaluate their performance.

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“…This distinction is very important, as random-field disorder is known to be much more detrimental to long-order range order than random-mass disorder. In the specific case of the 3-state Potts model, random-field is believed to completely kill the Potts transition in two dimensions, and to suppress it in three dimensions [43][44][45]. Thus, one generally expects random strain to tilt the balance between the competing vestigial charge-4e and nematic orders in favor of the former.…”

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confidence: 99%

Charge- 4e Superconductivity from Multicomponent Nematic Pairing: Application to Twisted Bilayer Graphene

Fernandes

2021

Phys. Rev. Lett.

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We show that unconventional nematic superconductors with multi-component order parameter in lattices with three-fold and six-fold rotational symmetries support a charge-4e vestigial superconducting phase above Tc. The charge-4e state, which is a condensate of four-electron bound states that preserve the rotational symmetry of the lattice, is nearly degenerate with a competing vestigial nematic state, which is non-superconducting and breaks the rotational symmetry. This robust result is the consequence of a hidden discrete symmetry in the Ginzburg-Landau theory, which permutes quantities in the gauge sector and in the crystalline sector of the symmetry group. We argue that random strain generally favors the charge-4e state over the nematic phase, as it acts as a random-mass to the former but as a random-field to the latter. Thus, we propose that twodimensional inhomogeneous systems displaying nematic superconductivity, such as twisted bilayer graphene, provide a promising platform to realize the elusive charge-4e superconducting phase.

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Approximate ground states of the random-field Potts model from graph cuts

Cited by 11 publications

References 72 publications

Massively parallel simulations for disordered systems

Massively parallel simulations for disordered systems

On the comparison of optimization algorithms for the random-field Potts model

Charge- 4e Superconductivity from Multicomponent Nematic Pairing: Application to Twisted Bilayer Graphene

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