Sequence of discrete spin models approximating the classical Heisenberg ferromagnet

Margaritis, Athanasios; Ódor, Géza; Patkós, A.

doi:10.1088/0305-4470/20/7/036

Cited by 6 publications

(4 citation statements)

References 7 publications

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“…Nienhuis et al showed that the cubic anisotropy is relevant to the O(3) symmetry on 2D lattice, and a nontrivial phase diagram was reported for the ferromagnetic case [8]. Margaritis et al confirmed the presence of the order-disorder phase transition in the discrete vector spin models with 12, 20, and 30 degrees of freedom on the square lattice and showed that the transition temperature is strongly dependent on the number of the local spin states [2]. Patrascioiu and Seiler performed a scaling analysis for the case of the icosahedral discretization and estimated the critical exponents assuming that the transition is of the second order [9].…”

Section: Introductionmentioning

confidence: 99%

“…It was shown that the calculated phase transition temperature coincides well with that of the 3D Heisenberg model. Margaritis et al considered a 12-state discrete vector model, which corresponds to the icosahedral symmetry, and also the 20-state one with the dodecahedral symmetry [2]. On the cubic lattice, it was shown that the 12-state model already well represent the phase transition of the 3D Heisenberg model.…”

Section: Introductionmentioning

confidence: 99%

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Phase diagram of a truncated tetrahedral model

2016

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Phase diagram of a discrete counterpart of the classical Heisenberg model, the truncated tetrahedral model, is analyzed on the square lattice, when the interaction is ferromagnetic. Each spin is represented by a unit vector that can point to one of the 12 vertices of the truncated tetrahedron, which is a continuous interpolation between the tetrahedron and the octahedron. Phase diagram of the model is determined by means of the statistical analog of the entanglement entropy, which is numerically calculated by the corner transfer matrix renormalization group method. The obtained phase diagram consists of four different phases, which are separated by five transition lines. In the parameter region, where the octahedral anisotropy is dominant, a weak first-order phase transition is observed.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Phase diagram of a truncated tetrahedral model

2016

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“…We perform fits similar to those performed in section IV C. Here we only include the data obtained for λ = 5.0 and 5.2. Furthermore we fix the value of Ū * 4 to that obtained in section IV C. For ξ 2nd /L = 0.56404 we get λ * = 5.19(2) [6], while for Z a /Z p = 0.19477 we get λ * = 5.14(2) [6], where the error in [] is due to the uncertainty of Ū * 4 . Our final estimate λ * = 5.17 (11) (A5) is chosen such that both estimates, including their errors are covered.…”

Section: Finite Size Scaling Estimate Of the Exponent ηmentioning

confidence: 99%

“…In addition (0, 0, 0) might be assumed. The idea to use a discrete subset of the sphere as values of the field variable is rather old [5,6], however received little attention. Note that the field variable is also referred to as spin.…”

Section: Introductionmentioning

confidence: 99%

Monte Carlo study of a generalized icosahedral model on the simple cubic lattice

Hasenbusch

2020

Preprint

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We study the critical behavior of a generalized icosahedral model on the simple cubic lattice.In addition to twelve vectors of unit length which are given by the normalized vertices of the icosahedron, the field variable is allowed to take the value (0, 0, 0). There is a parameter D that controls the density of zeros. For a certain range of D, the model undergoes a second order phase transition. On the critical line, O(3) symmetry emerges. Furthermore, we demonstrate that within this range, there is a value, where leading corrections to scaling vanish. We perform Monte Carlo simulations for lattices of a linear size up to L = 400 by using a hybrid of local Metropolis and cluster updates. The motivation to study this particular model is mainly of technical nature.Less memory and CPU time are needed than for a model with O(3) symmetry at the microscopic level. As the result of a finite size scaling analysis we obtain ν = 0.71164(10), η = 0.03784(5) and ω = 0.759(2) for the critical exponents of the three-dimensional Heisenberg universality class. The estimate of the irrelevant RG-eigenvalue that is related with the breaking the O(3) symmetry is

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Analysis of the Migdal transformation for models with planar spins on a two-dimensional lattice

Sokalski

Ruijgrok

Schoenmaker

1987

Physica A: Statistical Mechanics and its Applications

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By numericaland analytical investigations we show that the bond-moving transformation of Migdal for planar spins on a two-dimensional lattice possesses a very rich structure. We find an infinite hierarchy of one-, three-and higher-dimensional fixed spaces. In addition to phase transitions of the KosterlitzzThouless-type, we find Ising-like transitions, for which the critical exponents are the same as those of the q-state Potts model in the Migdal approximation. These critical exponents are constant within each fixed space. The phase diagram is constructed for two specially chosen potentials.

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Sequence of discrete spin models approximating the classical Heisenberg ferromagnet

Cited by 6 publications

References 7 publications

Phase diagram of a truncated tetrahedral model

Phase diagram of a truncated tetrahedral model

Monte Carlo study of a generalized icosahedral model on the simple cubic lattice

Analysis of the Migdal transformation for models with planar spins on a two-dimensional lattice

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