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arXiv:cond-mat/0012110 · Physical Review Letters

Ferromagnetic Phase Transition in a Heisenberg Fluid: Monte Carlo Simulations and Fisher Corrections to Scaling

I. M. Mryglod, I. P. Omelyan, R. Folk

Published Apr 2, 2001• 28 citations
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Abstract

The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations from the expected lattice values similar to those obtained previously. This puzzle is clarified by proving the importance of the leading correction to the scaling that appears due to Fisher renormalization with the critical exponent equal to the absolute value of the specific heat exponent alpha. The appearance of such new corretions to scaling is a general feature of systems with constraints.

DOI
10.1103/physrevlett.86.3156

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The magnetic phase transition in a Heisenberg fluid is studied by means of the finite size scaling technique. We find that even for larger systems, considered in an ensemble with fixed density, the critical exponents show deviations from the expected lattice values similar to those obtained previously. This puzzle is clarified by proving the importance of the leading correction to the scaling that appears due to Fisher renormalization with the critical exponent equal to the absolute value of the specific heat exponent alpha. The appearance of such new corretions to scaling is a general feature of systems with constraints.
The Ising fluid we have investigated is a system of hard spheres which carry an Ising spin. A short range ferromagnetic potential acts between particles. A renormalization group study of the model, based on the hierarchical reference theory of fluids, gives quantitative predictions on the phase diagram and the phase boundaries. The model can show two distinct phase transitions: a magnetic order-disorder transition and a liquid-vapor phase separation which meet at a tricritical point. The critical properties of the magnetic transition have been studied by Monte Carlo simulations at two densities in systems with up to 4000 particles. The locations of the critical points are in good agreement with the theoretical estimates. However, a finite-size scaling analysis shows effective critical exponents which deviate from the expected Ising values. These discrepancies resemble the analogous result of a previous numerical study of Heisenberg fluids. Here they are interpreted as due to crossover phenomena, partly related to Fisher exponent renormalization induced by the presence of noncritical density fluctuations.
We have simulated a fluid of particles which carry a Heisenberg spin and interact via a Heisenberg-like interaction. The fluid displays a magnetic order-disorder transition, which we studied by varying the temperature at a fixed particle density. We located the transition and estimated critical exponents by means of a finite-size scaling analysis. The exponents differ by a small but significant amount from the ones for the lattice Heisenberg model. \textcopyright{} 1996 The American Physical Society.
We have performed Monte Carlo simulations of the ferromagnetic order-disorder transition in an off-lattice version of the Heisenberg model. Varying the temperature at a fixed density, we located the transition for three different densities by means of a finite-size scaling analysis. The obtained critical exponents differ from those for the lattice Heisenberg model. Although the limited size of our systems warrants caution, the results question whether the lattice and the off-lattice model are in the same universality class.
Using Monte Carlo simulation techniques, we study the ferromagnetic order-disorder phase transition in Ising spin fluids with hard-core Yukawa interaction truncated at various cutoff radii r{c}. We focus our interest on the dependence of critical quantities such as the Binder cumulant and various exponent ratios on the value of r{c}, and on the question whether the Fisher-renormalized exponents expected for such systems can be observed in the simulations. It turns out that the corrections to scaling decaying with a rather small exponent prevent reaching the asymptotic region with the computational power available. Thus, we observe only effective exponents, with different (nonuniversal) values depending on the cutoff radius. The same behavior is also found for the critical Binder cumulant. Nevertheless, an exact investigation of the effective susceptibility exponent gamma{eff} as a function of temperature seems to point towards a Fisher-renormalized value. For two selected cutoff radii, the critical temperature is determined more accurately using, in addition to the cumulant crossing technique, the scanning technique and the shifting technique, taking into account corrections to scaling. Simulations of Ising fluids with constant cutoff radius and varying Yukawa-tail screening lengths lambda also show a nonuniversal dependence of U{c} on lambda. Finally, we have performed simulations of the Ising lattice model with increasing number of couplings which show the expected asymptotic behavior, independent of the range of interactions.
The influence of a thermodynamic constraint on the critical finite-size scaling behavior of three-dimensional Ising and XY models is analyzed by Monte-Carlo simulations. Within the Ising universality class constraints lead to Fisher renormalized critical exponents, which modify the asymptotic form of the scaling arguments of the universal finite-size scaling functions. Within the XY universality class constraints lead to very slowly decaying corrections inside the scaling arguments, which are governed by the specific heat exponent alpha. If the modification of the scaling arguments is properly taken into account in the scaling analysis of the data, finite-size scaling functions are obtained, which are independent of the constraint as anticipated by analytic theory.