In typical one-dimensional models the Mermin-Wagner theorem forbids long range order, thus preventing finite-temperature phase transitions. We find a finite-temperature phase transition for a homogeneous system of attractive bosons in one dimension. The low-temperature phase is characterized by a quantum bright soliton without long range order; the high-temperature phase is a free gas. Numerical calculations for finite particle numbers show a specific heat scaling as $N^2$ , consistent with a vanishing transition region in the thermodynamic limit.In typical one-dimensional models the Mermin-Wagner theorem forbids long range order, thus preventing finite-temperature phase transitions. We find a finite-temperature phase transition for a homogeneous system of attractive bosons in one dimension. The low-temperature phase is characterized by a quantum bright soliton without long range order; the high-temperature phase is a free gas. Numerical calculations for finite particle numbers show a specific heat scaling as $N^2$, consistent with a vanishing transition region in the thermodynamic limit.

arXiv:1610.09070Oct 28, 20162 citations

Phase transitions in ideal and weakly interacting Bose gases with a finite number of particles confined in a box

Jian-hui Wang, Yong-li Ma

We generalize the scheme to characterize phase transitions of finite systems in a complex temperature plane and approach the classifications of phase transitions in ideal and weakly interacting Bose gases of a finite number of particles, confined in a cubic box of volume L3 with different boundary conditions. For this finite ideal Bose system, by extending the classification parameters to all regions, we predict that the phase transition for periodic boundary conditions is of second order, while the transition in Dirichlet boundary conditions is of first order. For a weakly interacting Bose gas with periodic boundary conditions, we discuss the effects of finite particle numbers and inter-particle interactions on the nature of the phase transitions. We show that this homogenous weakly interacting Bose gas undergoes a second-order phase transition, which is in accordance with universality arguments for infinite systems. We also discuss the dependence of transition temperature on interaction strengths and particle numbers.We generalize the scheme to characterize phase transitions of finite systems in a complex temperature plane and approach the classifications of phase transitions in ideal and weakly interacting Bose gases of a finite number of particles, confined in a cubic box of volume L3 with different boundary conditions. For this finite ideal Bose system, by extending the classification parameters to all regions, we predict that the phase transition for periodic boundary conditions is of second order, while the transition in Dirichlet boundary conditions is of first order. For a weakly interacting Bose gas with periodic boundary conditions, we discuss the effects of finite particle numbers and inter-particle interactions on the nature of the phase transitions. We show that this homogenous weakly interacting Bose gas undergoes a second-order phase transition, which is in accordance with universality arguments for infinite systems. We also discuss the dependence of transition temperature on interaction strengths and particle numbers.

Journal of Physics B Atomic Molecular and Optical PhysicsDec 4, 20099 citations

Perspectives from the theory of phase transitions

G. Toulouse

Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento BSep 1, 1974111 citations

First-Order Phase Transitions

Wolfhard Janke E

Springer eBooksJan 1, 200333 citations

Phase transitions in magnetic clusters and other finite systems

Heinrich Stamerjohanns

This cumulative dissertation consists of seven articles dealing with phase transitions of magnetic clusters or other finite systems. We show that phase transitions in finite systems, which can be experimentally seen only in floppy humps of the specific heat or the magnetic susceptibility, can be quantitatively described by an analysis of an optimized estimation of the probability distribution of the system states combined with Landau free energy, or by analyzing the partition function in the complex temperature plane, or other complex-time response functions such as the complex specific heat. We show that new efficient methods, such as the Ferrenberg analysis, not applicable to infinite systems, can be applied to finite systems, even if the systems have more than one external parameter. With an Optimized Multidimensional Data Analysis of histograms produced by canonical Monte Carlo simulations, we are able to compute the phase behaviour of finite magnetic systems over a wide temperature and magnetic field range just by determining observables at a few given temperatures and magnetic fields.This cumulative dissertation consists of seven articles dealing with phase transitions of magnetic clusters or other finite systems. We show that phase transitions in finite systems, which can be experimentally seen only in floppy humps of the specific heat or the magnetic susceptibility, can be quantitatively described by an analysis of an optimized estimation of the probability distribution of the system states combined with Landau free energy, or by analyzing the partition function in the complex temperature plane, or other complex-time response functions such as the complex specific heat. We show that new efficient methods, such as the Ferrenberg analysis, not applicable to infinite systems, can be applied to finite systems, even if the systems have more than one external parameter. With an Optimized Multidimensional Data Analysis of histograms produced by canonical Monte Carlo simulations, we are able to compute the phase behaviour of finite magnetic systems over a wide temperature and magnetic field range just by determining observables at a few given temperatures and magnetic fields.

Jan 1, 20020 citations

N^2

, consistent with a vanishing transition region in the thermodynamic limit.