Topic
Ising model
About: Ising model is a research topic. Over the lifetime, 25508 publications have been published within this topic receiving 555000 citations.
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TL;DR: In this paper, the authors propose and investigate the potential of polariton graphs as an efficient analogue simulator for finding the global minimum of the XY model by imprinting polariton condensate lattices of bespoke geometries.
Abstract: The vast majority of real-life optimization problems with a large number of degrees of freedom are intractable by classical computers, since their complexity grows exponentially fast with the number of variables. Many of these problems can be mapped into classical spin models, such as the Ising, the XY or the Heisenberg models, so that optimization problems are reduced to finding the global minimum of spin models. Here, we propose and investigate the potential of polariton graphs as an efficient analogue simulator for finding the global minimum of the XY model. By imprinting polariton condensate lattices of bespoke geometries we show that we can engineer various coupling strengths between the lattice sites and read out the result of the global minimization through the relative phases. Besides solving optimization problems, polariton graphs can simulate a large variety of systems undergoing the U(1) symmetry-breaking transition. We realize various magnetic phases, such as ferromagnetic, anti-ferromagnetic, and frustrated spin configurations on a linear chain, the unit cells of square and triangular lattices, a disordered graph, and demonstrate the potential for size scalability on an extended square lattice of 45 coherently coupled polariton condensates. Our results provide a route to study unconventional superfluids, spin liquids, Berezinskii–Kosterlitz–Thouless phase transition, and classical magnetism, among the many systems that are described by the XY Hamiltonian.
278 citations
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TL;DR: In this article, the dependence of the shift in critical temperature ΔTc, critical field, etc., on the film thickness D, and on the nature of the walls as modeled by a surface field or chemical potential h1 which acts near the walls and leads to preferential adsorption of one of the bulk phases is discussed.
Abstract: Critical behavior in thin films is discussed with attention to the example of phase separation in binary fluid mixtures between parallel plates. The analyses focus on the dependence of the shift in critical temperature ΔTc, critical field, etc., on the film thickness D, and on the nature of the walls as modeled by a surface field or chemical potential h1 which acts near the walls and leads to preferential adsorption of one of the bulk phases. Mean field theory for an Ising/lattice‐gas model is utilized and the resulting asymptotic scaling functions for the shifts ΔTc etc. are computed within Landau theory by analytic and numerical methods. Series analyses for simple cubic lattice Ising model films with h1=0 are used to estimate universal features of three‐dimensional systems: specifically, if ξ(ΔT) is the bulk correlation length, determined, say, via scattering experiments, at ΔT=T−T∞c≳0 then the shift ratio D/ξ(‖ΔTc‖) is about 2.89 for h1=0 but 4.61 for h1→∞, compared with mean field values π and 5.0699....
278 citations
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TL;DR: The partition-functions-per-site k-approximation of several two-dimensional models (notably the eight-vertex, self-dual Potts and hard-hexagon models) can be easily obtained by using an inversion relation for local transfer matrices, together with symmetry and analyticity properties as discussed by the authors.
Abstract: The partition-functions-per-siteκ of several two-dimensional models (notably the eight-vertex, self-dual Potts and hard-hexagon models) can be easily obtained by using an inversion relation for local transfer matrices, together with symmetry and analyticity properties. This technique is discussed, the analyticity properties compared, and some equivalences (and nonequivalences) pointed out. In particular, the critical hard-hexagon model is found to have the sameκ as the self-dualq-state Potts model, withq=(3 + √5)/2 = 2.618 .... The Temperley-Lieb equivalence between the Potts and six-vertex models is found to fail in certain nonphysical antiferromagnetic cases.
277 citations
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TL;DR: In this article, a modification of the projected entangled-pair states (PEPS) algorithm was proposed to compute the ground state of quantum systems on an infinite two-dimensional lattice.
Abstract: An extension of the projected entangled-pair states (PEPS) algorithm to infinite systems, known as the iPEPS algorithm, was recently proposed to compute the ground state of quantum systems on an infinite two dimensional lattice. Here we investigate a modification of the iPEPS algorithm, where the environment is computed using the corner transfer matrix renormalization group (CTMRG) method, instead of using one-dimensional transfer matrix methods as in the original proposal. We describe a variant of the CTMRG that addresses different directions of the lattice independently, and use it combined with imaginary time evolution to compute the ground state of the two dimensional quantum Ising model. Near criticality, the modified iPEPS algorithm is seen to provide a better estimation of the order parameter and correlators.
277 citations
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TL;DR: In this paper, the authors used universal nonequilibrium dynamics and phenomenologically motivated values for the necessary nonuniversal quantities to estimate how much the growth of the QCD phase diagram is slowed.
Abstract: The QCD phase diagram may feature a critical end point at a temperature T and baryon chemical potential {mu} which is accessible in heavy-ion collisions. The universal long wavelength fluctuations which develop near this Ising critical point result in experimental signatures which can be used to find the critical point. The magnitude of the observed effects depends on how large the correlation length {xi} becomes. Because the matter created in a heavy-ion collision cools through the critical region of the phase diagram in a finite time, critical slowing down limits the growth of {xi}, preventing it from staying in equilibrium. This is the fundamental nonequilibrium effect which must be calculated in order to make quantitative predictions for experiment. We use universal nonequilibrium dynamics and phenomenologically motivated values for the necessary nonuniversal quantities to estimate how much the growth of {xi} is slowed. (c) 2000 The American Physical Society.
276 citations