Finite size scaling investigations in the quantum $\phi^4$-model with long-range interaction

TL;DR

This paper investigates the critical behavior of the quantum $^4$ model with long-range interactions, analyzing finite size and temperature effects on correlation length and critical amplitudes across various dimensions.

Contribution

It provides a detailed finite size scaling analysis of the quantum $^4$ model with long-range interactions in the large n-limit, including new results for different dimensional regimes.

Findings

Calculated correlation length and critical amplitudes.

Analyzed finite size shift effects.

Identified scaling regimes depending on temperature and size.

Abstract

In this paper, we study in details the critical behavior of the ${\cal O}(n)$ quantum $\phi^4$ model with long-range interaction decaying with the distances r by a power law as $r^{-d-\sigma}$ in the large n-limit. The zero-temperature critical behavior is discussed. Its alteration by the finite temperature and/or finite sizes in the space is studied. The scaling behaviours are studied in different regimes depending upon whether the finite temperature or the finite sizes of the system is leading. A number of results for the correlation length, critical amplitudes and the finite size shift, for different dimensionalities between the lower $d_<=\sigma/2$ and the upper $d_>=3\sigma/2$ critical dimensions, are calculated.