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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: A systematic approximation scheme, based on a global stationarity condition, is introduced and this scheme is used for an accurate determination of universal ratios of amplitudes, and a comparison with other theoretical and experimental determinations of universal quantities is presented.
Abstract: High-temperature series are computed for a generalized three-dimensional Ising model with arbitrary potential. Three specific "improved" potentials (suppressing leading scaling corrections) are selected by Monte Carlo computation. Critical exponents are extracted from high-temperature series specialized to improved potentials, achieving high accuracy; our best estimates are gamma=1.2371(4), nu=0.630 02(23), alpha=0.1099(7), eta=0.0364(4), beta=0.326 48(18). By the same technique, the coefficients of the small-field expansion for the effective potential (Helmholtz free energy) are computed. These results are applied to the construction of parametric representations of the critical equation of state. A systematic approximation scheme, based on a global stationarity condition, is introduced (the lowest-order approximation reproduces the linear parametric model). This scheme is used for an accurate determination of universal ratios of amplitudes. A comparison with other theoretical and experimental determinations of universal quantities is presented.
119 citations
TL;DR: An active Ising model in which spins both diffuse and align on lattice in one and two dimensions is considered, showing that this theoretical prediction holds in 2D whereas the fluctuations alter the transition in 1D, preventing, for instance, any spontaneous symmetry breaking.
Abstract: We consider an active Ising model in which spins both diffuse and align on lattice in one and two dimensions. The diffusion is biased so that plus or minus spins hop preferably to the left or to the right, which generates a flocking transition at low temperature and high density. We construct a coarse-grained description of the model that predicts this transition to be a first-order liquid-gas transition in the temperature-density ensemble, with a critical density sent to infinity. In this first-order phase transition, the magnetization is proportional to the liquid fraction and thus varies continuously throughout the phase diagram. Using microscopic simulations, we show that this theoretical prediction holds in 2D whereas the fluctuations alter the transition in 1D, preventing, for instance, any spontaneous symmetry breaking.
119 citations
TL;DR: In this paper, a long-range ferromagnetic interaction between two spins/rotors in units of lattice spacing was considered and the long-term behavior of the interaction drastically modifies the universal critical behaviour of the system.
Abstract: We investigate the zero-temperature and finite-temperature phase transitions of quantum Ising and quantum rotor models. We here assume a long-range (falling off as ${1/r}^{d+\ensuremath{\sigma}},$ where r is the distance between two spins/rotors in units of lattice spacing) ferromagnetic interaction among the spins or rotors. We find that the long-range behavior of the interaction drastically modifies the universal critical behavior of the system. The corresponding upper critical dimension and the hyperscaling relation and exponents associated with the quantum transition are modified and, as expected, they attain values of short-range system when $\ensuremath{\sigma}=2.$ The dynamical exponent varies continuously as the parameter \ensuremath{\sigma} and is unity for $\ensuremath{\sigma}=2.$ The one-dimensional long-range quantum Ising system shows a phase transition at $T=0$ for all values of \ensuremath{\sigma}. The most interesting observation is that the phase diagram for $\ensuremath{\sigma}=d=1$ shows a line of Kosterlitz-Thouless transition at finite temperature even though the $T=0$ transition is a simple order-disorder transition. These finite temperature transitions are studied near the phase boundary using renormalisation group equations and a region with diverging susceptibility is located. We have also studied one-dimensional quantum rotor model which exhibits a rich and interesting transition behavior depending upon the parameter \ensuremath{\sigma}. We explore the phase diagram extending the short-range quantum nonlinear \ensuremath{\sigma} model renormalisation group equations to the present case.
119 citations
TL;DR: In this paper, the possibility of a phase transition in an infinite simple random-cluster model (0 ≤ p ≤ 1, k ≥ 1), including the percolation model and the ferromagnetic Ising and Ashkin-Teller-Potts model, is studied by means of several criteria for large range connectivity.
119 citations
TL;DR: In this paper, a theoretical investigation of the possible occurrence of surface modes in semi-infinite ferroelectric materials is made, and three different approaches are used: (1) a microscopic pseudo-spin theory based on the Ising model in a transverse field, (2) a macroscopic Landau theory in which surface effects can be introduced phenomenologically, and (3) a polariton model appropriate to the very long wavelength region.
Abstract: A theoretical investigation is made of the possible occurrence of surface modes in semi-infinite ferroelectric materials. Three different approaches are used: (1) a microscopic pseudo-spin theory based on the Ising model in a transverse field, (2) a macroscopic Landau theory in which surface effects can be introduced phenomenologically, and (3) a polariton model appropriate to the very long wavelength region. Existence conditions and dispersion relations are deduced for the localised surface modes, which are predicted by all three methods. The results are illustrated by means of numerical examples. Methods (1) and (2) are found to give rise to similar results in certain limits, and the authors are able to establish a formal relationship between the two approaches. The applicability of the theoretical models to real ferroelectrics is discussed, and some experimental techniques by which the surface modes might be detected are suggested.
119 citations