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

Abstract

In this paper, we study in details the critical behavior of the $\mathcal{O}(n)$ quantum ${\varphi }^4$ 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.

22 pages

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