Classification of phase transitions of finite Bose-Einstein condensates in power-law traps by Fisher zeros

Abstract

We present a detailed description of a classification scheme for phase transitions in finite systems based on the distribution of Fisher zeros of the canonical partition function in the complex temperature plane. We apply this scheme to finite Bose-systems in power law traps within a semi-analytic approach with a continuous one-particle density of states Ω(E) ∼ E d−1 for different values of d and to a three dimensional harmonically confined ideal Bose-gas with discrete energy levels. Our results indicate that the order of the Bose-Einstein condensation phase transition sensitively depends on the confining potential.

Lee–Yang zeros and two-time spin correlation function

“…1). According to (14) the time correlation function for spin σ 0 is related with partition function of two other spins described by Hamiltonian (17) in complex magnetic field (15). The partition function of this Hamiltonian reads…”

“…Studies of zeros of partition function for spin systems have attracted much attention (see, for instance, [9,10,11,12,13,14] and references therein). At the same time there are essentially smaller number of papers devoted to studies of zeros of partition function of Bose systems (see, for instance, [15,16,17,18]) and Fermi systems (see, for instance, [20,21]).…”

Canonical statistics of trapped ideal and interacting Bose gases

“…On the basis of the same density of states a detailed study of the critical temperature and the ground state occupation number was given recently in [31]. In a thermodynamic equilibrium the deviation from the most probable value N p 0 is small, therefore we can use the approximation exp [−α (N, N 0 )] ≈ 1 − α (N, N 0 ).…”

“…This makes the interacting effect between atoms be much more important than above T c . The correction to the condensate fraction and critical temperature due to the interatomic interaction has been discussed within grand canonical ensemble [33][34][35][36] and canonical ensemble [37,31]. In this section we investigate the role of interaction on the condensate fluctuations of a weakly interacting Bose gas.…”

Deceptive Signals of Phase Transitions in Small Magnetic Clusters

“…However, they are not able to determine the order of the phase transition. Recently, we have proposed a classification scheme based on the distribution of zeros of the analytically continued canonical partition function Z͑B͒, with B b 1 it͑b 1͞T͒, in the complex temperature plane [11][12][13][14].The basic principle of the description of phase transitions by the zeros of the partition function is the product theorem of Weierstrass and the theorem of Mittag-Leffler which relate integral functions to their zeros [15]. Applying these theorems, the canonical partition function can be written as…”