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Proceedings of XXIIIrd International Symposium on Lattice Field Theory — PoS(LAT2005)

Quenched Disordered Ferromagnets

Wolfhard Janke E, Bertrand Berche, Christophe Chatelain, Pierre-Emmanuel Berche, Meik Hellmund

Published Dec 14, 2005• 4 citations
Publisher

Abstract

We review and compare different approaches for studying the influence of quenched, random disorder in three-dimensional Ising and Potts models for ferromagnets subject to impurities.From a theoretical view point, field theoretic renormalization group studies provide quite accurate results.Experiments carried out on crystalline mixtures of compounds lead to measurements of criticial exponents as accurate as three digits.Numerically, extensive Monte Carlo simulations are shown to be of comparable accuracy.Finally, we also discuss recently generated high-temperature series expansions for the free energy and susceptibility.Within this approach, using the star-graph expansion technique, quenched disorder averages can be calculated exactly while keeping the disorder strength p as well as the dimension d as symbolic parameters.

DOI
10.22323/1.020.0018

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We review and compare different approaches for studying the influence of quenched, random disorder in three-dimensional Ising and Potts models for ferromagnets subject to impurities.From a theoretical view point, field theoretic renormalization group studies provide quite accurate results.Experiments carried out on crystalline mixtures of compounds lead to measurements of criticial exponents as accurate as three digits.Numerically, extensive Monte Carlo simulations are shown to be of comparable accuracy.Finally, we also discuss recently generated high-temperature series expansions for the free energy and susceptibility.Within this approach, using the star-graph expansion technique, quenched disorder averages can be calculated exactly while keeping the disorder strength p as well as the dimension d as symbolic parameters.
We discuss different approaches to the study of the effect of disorder in the three-dimensional Ising model.From the theoretical point of view, renormalization group calculations provide quite accurate results.Experiments carried out on crystalline mixtures of compounds lead to measurements as accurate as three digits on the values of critical exponents.Numerically, extensive Monte Carlo simulations then pretend to be of comparable accuracy.Life becomes complicated when details are compared between the three approaches.
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A study of the influence of different types of disorder on systems in the Ising universality class by employing both a dynamical field theory approach and extensive Monte Carlo simulations is presented. We reproduce some well-known results for the case of quenched disorder (random temperature and random field), and analyze the effect of four different types of time-dependent disorder scarcely studied so far in the literature. Some of them are of obvious experimental and theoretical relevance (as, for example, globally fluctuating temperatures or random fields). All the predictions coming from our field-theoretical analysis are fully confirmed by extensive simulations in two and three dimensions, and novel qualitatively different, non-Ising transitions are reported. Possible experimental setups designed to explore the described phenomenologies are also briefly discussed.
We study the combined effect of cubic anisotropy and quenched uncorrelated impurities on multicomponent spin models. For this purpose, we consider the field-theoretical approach based on the Ginzburg-Landau-Wilson ${\ensuremath{\varphi}}^{4}$ Hamiltonian with cubic-symmetric quartic interactions and quenched randomness coupled to the local energy density. We compute the renormalization-group functions to six loops in the fixed-dimension (d=3)(d=3)(d=3) perturbative scheme. The analysis of such high-order series provides an accurate description of the renormalization-group flow. The results are also used to determine the critical behavior of three-dimensional antiferromagnetic three- and four-state Potts models in the presence of quenched impurities.
In order to study the influence of quenched disorder on second-order phase transitions, high-temperature series expansions of the susceptibility and the free energy are obtained for the quenched bond-diluted Ising model in d=3−−5d=3--5d=3−−5 dimensions. They are analyzed using different extrapolation methods tailored to the expected singularity behaviors. In d=4d=4d=4 and 5 dimensions we confirm that the critical behavior is governed by the pure fixed point up to dilutions near the geometric bond percolation threshold. The existence and form of logarithmic corrections for the pure Ising model in d=4d=4d=4 are confirmed, and our results for the critical behavior of the diluted system are in agreement with the type of singularity predicted by renormalization group considerations. In three dimensions we find large crossover effects between the pure Ising, percolation, and random fixed points. We estimate the critical exponent of the susceptibility to be $\ensuremath{\gamma}=1.305(5)$ at the random fixed point.