Physical review. B, Condensed matter

First-order phase transition in the fcc Heisenberg antiferromagnet

H. T. Diep, Hikaru Kawamura

Published Oct 1, 1989• 78 citations

Abstract

The nature of the phase transition of the nearest-neighbor Heisenberg antiferromagnet on a fcc lattice is studied by means of Monte Carlo simulations. Using a finite-size scaling, the transition is shown to be unambiguously of first order. Evidence for a first-order transition in the corresponding XY model is also presented.

DOI: 10.1103/physrevb.40.7019

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Physical review. B, Condensed matter

First-order phase transition in the fcc Heisenberg antiferromagnet

H. T. Diep, Hikaru Kawamura

Published Oct 1, 1989• 78 citations

Publisher

Abstract

DOI: 10.1103/physrevb.40.7019

Related papers

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Alto Stemmer, Alfred Hüller

Using Monte Carlo methods we investigate the phase transition of an Ising system on the fcc lattice, with antiferromagnetic nearest-neighbor interaction $J$ and ferromagnetic next-nearest-neighbor interaction $\ensuremath{\alpha}J$ for \ensuremath{\alpha} values up to 2. The scaling of the microcanonical entropy ${s}_{L}$ with system size $L$ agrees with the assumption of a first-order transition. Since the asymptotic behavior has not yet been reached, even for the largest systems with $L=40,$ our calculations cannot determine the order of the transition unambiguously.Using Monte Carlo methods we investigate the phase transition of an Ising system on the fcc lattice, with antiferromagnetic nearest-neighbor interaction $J$ and ferromagnetic next-nearest-neighbor interaction $\ensuremath{\alpha}J$ for \ensuremath{\alpha} values up to 2. The scaling of the microcanonical entropy ${s}_{L}$ with system size $L$ agrees with the assumption of a first-order transition. Since the asymptotic behavior has not yet been reached, even for the largest systems with $L=40,$ our calculations cannot determine the order of the transition unambiguously.

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The Physics of Metals and MetallographyApr 1, 20206 citations

Using Monte Carlo methods we investigate the phase transition of an Ising system on the fcc lattice, with antiferromagnetic nearest-neighbor interaction

J

and ferromagnetic next-nearest-neighbor interaction $\ensuremath{\alpha}J$ for \ensuremath{\alpha} values up to 2. The scaling of the microcanonical entropy

{s}_{L}

with system size

L

agrees with the assumption of a first-order transition. Since the asymptotic behavior has not yet been reached, even for the largest systems with

L=40,

our calculations cannot determine the order of the transition unambiguously.

The Ising antiferromagnet on a face-centered cubic (fcc) lattice with nearest-neighbor interaction only is well known to exhibit a macroscopic (exponential in the system size

L

) ground-state degeneracy. With increasing temperature, this degeneracy is expected to be lifted and the model undergoes a first-order phase transition. For a model with an exponential degeneracy in the whole low-temperature phase, it was recently found that the finite-size scaling behavior is governed by leading correction terms $\ensuremath{\sim}{L}^{\ensuremath{-}2}$ instead of $\ensuremath{\sim}{L}^{\ensuremath{-}3}$ as usual. To test the conjecture that such a transmuted behavior may effectively persist also for the fcc antiferromagnet up to some crossover system size, we have performed parallel multicanonical Monte Carlo simulations for lattices of linear size $L\ensuremath{\le}18$ with periodic boundary conditions and determined various inverse pseudo phase transition temperatures, as well as the extremal values of the specific heat and the energetic Binder parameter. We indeed find that, for the simulated lattice sizes, the conjectured transmuted finite-size scaling ansatz fits the data better than the standard ansatz. On this basis, we extrapolate for the transition temperature an estimate of

{T}_{0}=1.735047(46)

J

. These results are compared with earlier approximations of the model, in particular, the low-temperature series expansion and the Kikuchi tetrahedron approximation, and other Monte Carlo results. The spin-spin correlation function was measured in the disordered phase up to eight lattice spacings in the [100] direction. The correlation length at the transition is found to be $\ensuremath{\sim}2.5a$. The behavior of the correlation length is approximately mean-field-like.