Phase structure and critical behavior of lattice $\phi^4$ theory at different temperatures

Abstract

The Variational-Cumulant Expansion method is applied to investigate the phase structure and the critical behavior of lattice φ 4 theory at two different temperatures. The phase diagrams, the external current J as a function of the expectation value of the field operator φ L are calculated to the third order analytically. The critical behaviors of the expectation value φ L , the renormalized mass m R and m R / φ L are given and compared with the mean-field scaling laws with logarithmic scaling corrections. It is shown that, at a fixed bare coupling, the broken phase at a lower temperature might be restored at a higher temperature and a bound on the Higgs-boson mass at definite temperature can exist.

Quantum dynamics of phase transitions in broken symmetryλφ4field theory

“…Explicit Monte Carlo lattice calculations [33,34] have shown that indeed λφ 4 theory in two-dimensions and at zero temperature is non-trivial at least when the continuum limit is reached from the broken symmetry phase, and that the symmetry is fully restored at high temperature. It is known however that approximate lattice calculations (such as the variationalcumulant expansion method [35,36]), which are designed to study scalar φ 4 theory in 3+1 dimensions on the lattice, may erroneously indicate the presence of a secondorder phase transition at finite temperature in 1+1 dimensions. This is probably due to the fact that the expansion is only carried out to third order.…”

Unifying Static and Dynamic Properties in 3D Quantum Antiferromagnets

“…Although there exists a wealth of analytical results detailing the theory of logarithmic corrections [1,[5][6][7][8][9][10], discerning them in experimental measurements is a hugely demanding task requiring datasets spanning many orders of magnitude in parameter space near a QPT. Similarly, their numerical determination in lattice simulations is a delicate and highly computationally intensive proposition.…”

Unifying static and dynamic properties in three-dimensional quantum antiferromagnets

“…Although there exists a wealth of analytical results detailing the theory of logarithmic corrections [1,[5][6][7][8][9][10], discerning them in experimental measurements is a hugely demanding task requiring datasets spanning many orders of magnitude in parameter space near a QPT. Similarly, their numerical determination in lattice simulations is a delicate and highly computationally intensive proposition.…”