An improved lattice measurement of the critical coupling in phi^4_2 theory

TL;DR

This paper uses Monte Carlo simulations to refine the measurement of the critical coupling in (1+1)-dimensional phi^4 theory, revealing a logarithmic dependence on lattice coupling and providing a more accurate continuum value.

Contribution

It presents an improved lattice measurement of the critical coupling in phi^4_2 theory, highlighting a logarithmic dependence and resolving discrepancies with earlier estimates.

Findings

Critical coupling constant is logarithmically dependent on lattice coupling.

Continuum critical coupling value is estimated as 10.8(1).

Results align with analytical expectations and previous but less precise studies.

Abstract

We use Monte Carlo simulations to obtain an improved lattice measurement of the critical coupling constant [lambda / mu^2]_crit for the continuum (1 + 1)-dimensional (lambda / 4) phi^4 theory. We find that the critical coupling constant depends logarithmically on the lattice coupling, resulting in a continuum value of [lambda / mu^2]_crit = 10.8(1), in considerable disagreement with the previously reported [lambda / mu^2]_crit = 10.26(8). Although this logarithmic behavior was not observed in earlier lattice studies, it is consistent with them, and expected analytically.