The effective potential, critical point scaling and the renormalization group

TL;DR

This paper demonstrates how Monte Carlo simulations combined with renormalization group techniques can effectively evaluate the potential near phase transitions in field theories, capturing all relevant scaling features.

Contribution

It introduces a method to extract the effective potential from Monte Carlo data using renormalization group results, applicable to systems near criticality.

Findings

Successful extraction of the effective potential from Ising model simulations

Inclusion of all scaling features in the analysis

Validation of the method with Monte Carlo and RG results

Abstract

The desirability of evaluating the effective potential in field theories near a phase transition has been recognized in a number of different areas. We show that recent Monte Carlo simulations for the probability distribution for the order parameter in an equilibrium Ising system, when combined with low-order renormalization group results for an ordinary $\phi^4$ system, can be used to extract the effective potential. All scaling features are included in the process.