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Journal of Physics A Mathematical and General

Fluctuations in dilute antiferromagnets: Curie-Weiss models

João Amaro de Matos, J. A. Baêta Segundo, J F Perez

Published May 21, 1992• 3 citations
Publisher

Abstract

The authors compute the fluctuations of the order parameter in the Curie-Weiss version of a site-dilute antiferromagnet. Their results show: (i) Gaussian fluctuations away from criticality or at a first-order critical point with sample and thermal fluctuations contributing in same order; (ii) Non-Gaussian fluctuations with critical exponents modified by the presence of dilution at the second-order critical point. In this case sample-induced fluctuations are enhanced to dominate over the thermal ones. Critical exponents are the same as in the Curie-Weiss random field Ising model.

DOI
10.1088/0305-4470/25/10/011

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The authors compute the fluctuations of the order parameter in the Curie-Weiss version of a site-dilute antiferromagnet. Their results show: (i) Gaussian fluctuations away from criticality or at a first-order critical point with sample and thermal fluctuations contributing in same order; (ii) Non-Gaussian fluctuations with critical exponents modified by the presence of dilution at the second-order critical point. In this case sample-induced fluctuations are enhanced to dominate over the thermal ones. Critical exponents are the same as in the Curie-Weiss random field Ising model.
We perform intensive numerical simulations of the three-dimensional site-diluted Ising antiferromagnet in a magnetic field at high values of the external applied field. Even if data for small lattice sizes are compatible with second-order criticality, the critical behavior of the system shows a crossover from second-order to first-order behavior for large system sizes, where signals of latent heat appear. We propose ``apparent'' critical exponents for the dependence of some observables on the lattice size for a generic (disordered) first-order phase transition.
Changes in magnetic critical behaviour of quenched structurally-disordered magnets are usually exemplified in experiments and in MC simulations by diluted systems consisting of magnetic and non-magnetic components. In our study we aim to show that similar effects can be observed not only for diluted magnets with non-magnetic impurities but may be implemented, e.g., by the presence of two (and more) chemically different magnetic components as well. Therefore we consider a model of the structurally-disordered quenched magnet where all lattice sites are occupied by Ising-like spins of different lengths L. In such a random spin length Ising model, the length L of each spin is a random variable governed by the distribution function p(L). We demonstrate that this model belongs to the universality class of the site-diluted Ising model. This proves that both models are described by the same values of asymptotic critical exponents. However, their effective critical behaviour differs. As a case study, we consider a quenched mixture of two different magnets with values of elementary magnetic moments L1=1 and L2=s, and of concentration c and 1−c, correspondingly. We apply field-theoretical renormalization group approach to analyse the renormalization group flow for different initial conditions, triggered by s and c, and to calculate effective critical exponents further away from the fixed points of the renormalization group transformation. We show how the effective exponents are governed by difference in properties of the magnetic components.
The modern techniques of field theory applied to critical phenomena, are briefly discussed, with particular emphasis on the use of the e-expansion to extract the asymptotic behaviour in the critical region. The dimensional regularisation and minimal subtraction method of renormalisation, Introduced by 't Hooft and Veltman, is outlined. These methods, along with a Monte Carlo simulation on a highly parallel computer, are utilised in extracting information pertaining to the behaviour near criticality of the random, site-diluted Ising model. The universal ratio of the susceptibility amplitude above and below the critical temperature is determined to one higher order than previously in an ɛ-expansion, within the framework of the replica formalism. The calculation is performed using a Taylor expansion, in the number of replicas, of the transverse propagator appearing In the Hamiltonian, about the longitudinal. This higher order correction goes in the right direction for agreement with experiment. An extension of the formalism to embrace the presence of two sets of replica spins is used to derive the o(ɛ¹/²) term in an expansion of the additional static - correlation function, C⁽ˢ⁾(q), arising from the non-interchangeability of the thermal and configurational averages In the random model. The appearance of C(sl(q) in the structure factor Implies that results of neutron scattering experiments to measure the susceptibility amplitude ratio must be re-Interpreted. Finally, analysis of the properties of block spin variables In a Monte Carlo simulation Is used to determine the phase diagram and critical exponents In two-dimensions. Possible Interpretations of the observed evolution of the exponent ratio, ß/υ, under Increasing dilution are discussed.