Eur. Phys. J. B 14, 307-316 (2000)
https://doi.org/10.1007/s100510050134

Casimir amplitudes in a quantum spherical model with long-range interaction

¹ Georgy Nadjakov Institute of Solid State Physics - BAS, Tzarigradsko chaussée 72, 1784 Sofia, Bulgaria
² Institute of Mechanics - BAS, Acad. G. Bonchev St. bl. 4, 1113 Sofia, Bulgaria

Received: 3 June 1999
Revised: 16 August 1999
Published online: 15 March 2000

Abstract

A d-dimensional quantum model system confined to a general hypercubical geometry with linear spatial size L and "temporal size"1/T ( T - temperature of the system) is considered in the spherical approximation under periodic boundary conditions. For a film geometry in different space dimensions , where is a parameter controlling the decay of the long-range interaction, the free energy and the Casimir amplitudes are given. We have proven that, if , the Casimir amplitude of the model, characterizing the leading temperature corrections to its ground state, is . The last implies that the universal constant of the model remains the same for both short, as well as long-range interactions, if one takes the normalization factor for the Gaussian model to be such that . This is a generalization to the case of long-range interaction of the well-known result due to Sachdev. That constant differs from the corresponding one characterizing the leading finite-size corrections at zero temperature which for is .