Physical review. B, Condensed matter

Quenched bond-mixed cubic ferromagnet in a planar self-dual lattice: Critical behavior

André M. C. Souza, Constantino Tsallis, Ananias M. Mariz

Published May 1, 1993• 3 citations

Abstract

The critical behavior of the quenched bond-mixed ferromagnetic cubic model, on a planar self-dual hierarchical lattice, is investigated within a simple real-space renormalization group. We obtain the complete phase diagram of the system, exhibiting three phases. This phase diagram is believed to be of high precision for the square lattice. The correlation-length critical exponents and the universality classes are determined as well.

DOI: 10.1103/physrevb.47.11940

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Physical review. B, Condensed matter

Quenched bond-mixed cubic ferromagnet in a planar self-dual lattice: Critical behavior

André M. C. Souza, Constantino Tsallis, Ananias M. Mariz

Published May 1, 1993• 3 citations

Publisher

Abstract

DOI: 10.1103/physrevb.47.11940

Related papers

Criticality of the bond-diluted Ising ferromagnet in a semi-infinite simple-cubic lattice

L. R. da Silva, Constantino Tsallis, Enaldo F. Sarmento

We study the phase diagram and universality classes of the quenched bond-diluted spin-(1/2 Ising ferromagnet in a semi-infinite simple-cubic lattice with a (001) free surface. The approach (herein formulated for arbitrary values of the number of states q of the Potts model) is a real-space renormalization group which preserves two-spin correlation functions and uses clusters which have already proved to be very appropriate for the present structure. We observe that surface ferromagnetism persists below the two-dimensional (2D) percolation threshold ${p}_{c}^{2\mathrm{D}=(1/2}$ , in fact down to ${p}_{c}$ \ensuremath{\simeq}0.42. In addition to that we check that a conjectural extension of the Kasteleyn-Fortuin theorem is satisfied in the present particular case.We study the phase diagram and universality classes of the quenched bond-diluted spin-(1/2 Ising ferromagnet in a semi-infinite simple-cubic lattice with a (001) free surface. The approach (herein formulated for arbitrary values of the number of states q of the Potts model) is a real-space renormalization group which preserves two-spin correlation functions and uses clusters which have already proved to be very appropriate for the present structure. We observe that surface ferromagnetism persists below the two-dimensional (2D) percolation threshold ${p}_{c}^{2\mathrm{D}=(1/2}$, in fact down to ${p}_{c}$\ensuremath{\simeq}0.42. In addition to that we check that a conjectural extension of the Kasteleyn-Fortuin theorem is satisfied in the present particular case.

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{p}_{c}^{2\mathrm{D}=(1/2}

, in fact down to

{p}_{c}

\ensuremath{\simeq}0.42. In addition to that we check that a conjectural extension of the Kasteleyn-Fortuin theorem is satisfied in the present particular case.

L=48

. By employing a standard finite-size scaling method, the numerical values of the N\'eel temperature are determined with high precision as a function of the coupling ratio

r={J}_{2}/{J}_{1}

. Based on the estimated critical exponents, we find that the critical behavior of the considered model belongs to the pure classical three-dimensional

O(3)

Heisenberg universality class.

{\mathit{T}}_{\mathit{c}}

vanishes for values of the anisotropy parameter \ensuremath{\Delta}\ensuremath{\le}0.399, i.e., for small anisotropy the order is destroyed by quantum fluctuations at any finite temperature.

d

and have different phase diagram topologies at the multicritical points of the conjecture and even though the contributions to the conjecture from each lattice of the dual pair are strongly asymmetric. In all six phase diagrams, we find reentrance near the multicritical point. In the models with

d=2

or 1.5, the spin glass phase does not occur and the phase boundary between the ferromagnetic and paramagnetic phases is second order with a strong violation of universality.