# MC simulations of $O(2)\phi^4$ theory in three dimensions with worm algorithm

## TL;DR

This paper uses Monte Carlo simulations with a worm algorithm to study the critical behavior of the three-dimensional $O(2)\,^4$ theory, aiming to refine the estimate of the critical temperature correction for a weakly interacting Bose gas.

## Contribution

It provides a detailed Monte Carlo analysis of the $O(2)\,^4$ theory in three dimensions using a worm algorithm, focusing on critical properties relevant to Bose gases.

## Key findings

- Determined the ratio $ riangleraket{^2}_c/g$ near criticality.
- Estimated the first correction to the critical temperature of a weakly interacting Bose gas.
- Enhanced understanding of critical behavior in $O(2)^4$ lattice models.

## Abstract

We study the critical region of the $O(2)\,\phi^4$ theory by means of Monte Carlo simulations on the lattice. In particular we determine the ratio $\Delta\langle\phi^2\rangle_c/g$ in order to estimate the first correction to the critical temperature of a weak interacting Bose gas.