The type of the phase transition and coupling values in \lambda \phi^4 model

TL;DR

This study uses extensive lattice Monte Carlo simulations to analyze the nature of temperature-induced phase transitions in the  scalar field model, identifying the coupling threshold where the transition type changes.

Contribution

It provides the first detailed numerical determination of the coupling value at which the phase transition shifts from weak first-order to second order in the  model.

Findings

Weak first-order transition near the lower coupling bound.

Transition becomes second order as coupling increases.

Comparison with previous analytic and numeric results.

Abstract

The temperature induced phase transition is investigated in the one-component scalar field \phi^4 model on the lattice. Using the GPU cluster a huge amount of Monte Carlo simulation data is collected for a wide interval of coupling values. This gives a possibility to determine the low bound on the coupling constant \lambda_0 when the transition happens and investigate its type. We found that for the values of \lambda close to this bound a weak-first-order phase transition takes place. It converts into a second order one with the increase of \lambda. A comparison with the results obtained in analytic and numeric calculations by other authors is given.