Numerical Simulation of N-vector Spin Models in a Magnetic Field

TL;DR

This paper improves the parametrization of the magnetic equation of state for 3D N-vector spin models, enhancing the accuracy of critical phenomena descriptions relevant to superfluid and quark-gluon plasma transitions.

Contribution

It introduces a new, perturbation theory-inspired parametrization of the magnetic equation of state, fitted nonperturbatively to numerical data for better modeling.

Findings

Enhanced fit to numerical data of the equation of state

More accurate determination of critical amplitude ratios

Improved description of the pseudo-critical line

Abstract

Three-dimensional N-vector spin models may define universality classes for such diverse phenomena as i) the superfluid transition in liquid helium (currently investigated in the micro-gravity environment of the Space Shuttle) and ii) the transition from hadronic matter to a quark-gluon plasma, studied in heavy-ion collisions at the laboratories of Brookhaven and CERN. The models have been extensively studied both by field-theoretical and by statistical mechanical methods, including Monte Carlo simulations using cluster algorithms. These algorithms are applicable also in the presence of a magnetic field. Key quantities for the description of the transitions above -- such as universal critical amplitude ratios and the location of the so-called pseudo-critical line -- can be obtained from the models' magnetic equation of state, which relates magnetization, external magnetic field and temperature. Here we present an improved parametrization for the equation of state of the models, allowing a better fit to the numerical data. Our proposed form is inspired by perturbation theory, with coefficients determined nonperturbatively from fits to the data.