Liquid-vapor transition of systems with mean field universality class

TL;DR

This study investigates a system with mixed short-range and long-range interactions, demonstrating that it exhibits mean field critical behavior for any positive long-range component, with theoretical and simulation results aligning well for certain parameters.

Contribution

It introduces a combined potential model and compares theoretical predictions with simulations, confirming mean field universality class behavior for positive long-range interaction strength.

Findings

System belongs to the mean field universality class for any positive xi.

Theoretical approaches agree with simulations when xi^2 > 0.05.

Non-classical behavior observed only at xi=0.

Abstract

We have considered a system where the interaction, v(r) = v_IS(r) + xi^2 v_MF(r), is given as a linear combination of two potentials, each of which being characterized with a well-defined critical behavior: for v_IS(r) we have chosen the potential of the restricted primitive model which is known to belong to the Ising 3D (IS) universality class, while for v_MF(r) we have considered a long-range interaction in the Kac-limit, displaying mean field (MF) behavior. We study the performance of two theoretical approaches and of computer simulations in the critical region for this particular system and give a detailed comparison between theories and simulation of the critical region and the location of the critical point. Both, theory and simulation give evidence that the system belongs to the MF universality class for any positive value of xi and that it shows only non-classical behavior for xi=0. While in this limiting case theoretical approaches are known to fail, we find good agreement for the critical properties between the theoretical approaches and the simulations for xi^2 larger than 0.05.