Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physics B Atomic Molecular and Optical Physics

Finite-size scaling of the specific heat for a three-dimensional homogeneous weakly interacting Bose gas within a canonical statistics

Jian-hui Wang, Yong-li Ma

Published Aug 10, 2010• 5 citations
Publisher

Abstract

Within a canonical ensemble treatment, we study the finite-size scaling behaviour of the specific heat near the critical region for the weakly interacting Bose gases, and obtain the specific heat exponent α and correlation length exponent ν which agree well with experimental data and previous theoretical predictions. For the small and fixed interaction parameter an 1/3 with a being the scattering length and n the particle number density, we report for the first time that the dimensionless specific heats per particle c ( t , N ) for various system sizes ( L = ( N / n ) 1/3 in a square box potential) and reduced temperatures ( t = T / T c − 1) collapse onto a single form, and the borders of universality validity are obtained numerically. From scaling arguments, we study the interaction-induced shift of the transition temperature (Δ T c = T c − T 0 c ) and find that Δ T c / T 0 c = ban 1/3 with b = 0.42 ± 0.05, where T 0 c is the ideal-gas thermodynamic critical temperature. We also compare our findings with experimental and theoretical results for in cubic lattices, showing the very different behaviours for the two systems.

DOI
10.1088/0953-4075/43/17/175301

Related papers

Thermodynamics and finite-size scaling of homogeneous weakly interacting Bose gases within an exact canonical statistics

Jian-hui Wang, Yong-li Ma

The thermodynamic properties and finite-size scaling of weakly interacting Bose gases with a finite number of particles confined in a cubic box of volume ${L}^{3}$ with periodic boundary conditions are investigated theoretically based on an exact recursion relation for the canonical-ensemble partition function. In a similar manner to the case of an ideal Bose gas, the recursive scheme of the interacting finite system at any temperatures is established in the framework of the Bogoliubov theory. The temperature dependence of the condensate fraction and specific heat with different particles and interactions is obtained numerically. By defining two different transition temperatures of the finite systems, the effect of interactions on the transition temperatures yields the different and nonmonotonous behaviors. The finite-size scaling condensate fraction at the transition temperature for the systems is also discussed. It is shown that the calculated finite-size scaling is universally independent on the various system sizes and transition temperatures.

Physical Review A•Mar 5, 2009•33 citations

Critical temperature and thermodynamic properties of a homogeneous dilute weakly interacting Bose gas within the improved Hartree-Fock approximation at finite temperature

Nguyễn Văn Thụ, Thanh, Pham Duy

By means of Cornwall-Jackiw-Tomboulis effective action approach we investigate a homogeneous dilute weakly interacting Bose gas at finite temperature in vicinity of critical region. A longstanding debate, the shift of critical temperature, is considered and obtained in the universal form $ΔT_C/T_C^{(0)} = cn_0^{1/3}a_s$ with constants $c$ and $a$. The non-condensate fraction is contributed by quantum fluctuations as well as thermal exitations and can be expressed in sum of three terms. These terms correspond to the quantum fluctuations, thermal fluctuations and both. Indeed, the specific heat capacity and critical exponents are calculated and in excellent agreement with those in previous works and experimental data.

arXiv:2311.13822•Nov 23, 2023•0 citations

Bose-Einstein condensation temperature of a homogeneous weakly interacting Bose gas: Path integral Monte Carlo study

Kwangsik T. Nho, David Paul Landau

Using a finite-temperature path integral Monte Carlo simulation (PIMC) method and finite-size scaling, we have investigated the interaction-induced shift of the phase-transition temperature for Bose-Einstein condensation of homogeneous weakly interacting Bose gases in three dimensions, which is given by a proposed analytical expression ${T}_{c}={T}_{c}^{0}{1+{c}_{1}a{n}^{1∕3}+[{c}_{2}^{\ensuremath{'}}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(a{n}^{1∕3})+{c}_{2}^{\ensuremath{''}}]{a}^{2}{n}^{2∕3}+\mathrm{O}({a}^{3}n)}$, where ${T}_{c}^{0}$ is the critical temperature for an ideal gas, $a$ is the $s$-wave scattering length, and $n$ is the number density. We have used smaller number densities and more time slices than in the previous PIMC simulations [Gruter et al., Phys. Rev. Lett. 79, 3549 (1997)] in order to understand the difference in the value of the coefficient ${c}_{1}$ between their results and the (apparently) other reliable results in the literature. Our results show that ${({T}_{c}\ensuremath{-}{T}_{c}^{0})∕{T}_{c}^{0}}∕(a{n}^{1∕3})$ depends strongly on the interaction strength $a{n}^{1∕3}$ while the previous PIMC results are considerably flatter and smaller than our results. We obtain ${c}_{1}=1.32\ifmmode\pm\else\textpm\fi{}0.14$, in agreement with results from recent Monte Carlo methods of three-dimensional O(2) scalar ${\ensuremath{\phi}}^{4}$ field theory and variational perturbation theory.

arXiv:cond-mat/0404238•Physical Review A•Nov 18, 2004•56 citations

Critical Temperature of Interacting Bose Gases in Two and Three Dimensions

Sebastiano Pilati, S. Giorgini, Nikolay V. Prokof'ev

We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.

arXiv:0801.3424•Physical Review Letters•Apr 9, 2008•75 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.

Journal of Physics B Atomic Molecular and Optical Physics•Dec 4, 2009•9 citations

Transition temperature of the weakly interacting Bose gas: perturbative solution of the crossover equations in the canonical ensemble

Martin Wilkens, Fabrizio Illuminati, Meret Krämer

We compute the critical temperature T_c of a weakly interacting uniform Bose gas in the canonical ensemble, extending the criterion of condensation provided by the counting statistics for the uniform ideal gas. Using ordinary perturbation theory, we find in first order $(T_c-T_c^0)/T_c^0 = -0.93 aρ^{1/3}$, where T_c^0 is the transition temperature of the corresponding ideal Bose gas, a is the scattering length, and $ρ$ is the particle number density.

arXiv:cond-mat/0001422•Journal of Physics B Atomic Molecular and Optical Physics•Oct 5, 2000•30 citations
Within a canonical ensemble treatment, we study the finite-size scaling behaviour of the specific heat near the critical region for the weakly interacting Bose gases, and obtain the specific heat exponent α and correlation length exponent ν which agree well with experimental data and previous theoretical predictions. For the small and fixed interaction parameter an 1/3 with a being the scattering length and n the particle number density, we report for the first time that the dimensionless specific heats per particle c ( t , N ) for various system sizes ( L = ( N / n ) 1/3 in a square box potential) and reduced temperatures ( t = T / T c − 1) collapse onto a single form, and the borders of universality validity are obtained numerically. From scaling arguments, we study the interaction-induced shift of the transition temperature (Δ T c = T c − T 0 c ) and find that Δ T c / T 0 c = ban 1/3 with b = 0.42 ± 0.05, where T 0 c is the ideal-gas thermodynamic critical temperature. We also compare our findings with experimental and theoretical results for in cubic lattices, showing the very different behaviours for the two systems.
The thermodynamic properties and finite-size scaling of weakly interacting Bose gases with a finite number of particles confined in a cubic box of volume L3{L}^{3}L3 with periodic boundary conditions are investigated theoretically based on an exact recursion relation for the canonical-ensemble partition function. In a similar manner to the case of an ideal Bose gas, the recursive scheme of the interacting finite system at any temperatures is established in the framework of the Bogoliubov theory. The temperature dependence of the condensate fraction and specific heat with different particles and interactions is obtained numerically. By defining two different transition temperatures of the finite systems, the effect of interactions on the transition temperatures yields the different and nonmonotonous behaviors. The finite-size scaling condensate fraction at the transition temperature for the systems is also discussed. It is shown that the calculated finite-size scaling is universally independent on the various system sizes and transition temperatures.
By means of Cornwall-Jackiw-Tomboulis effective action approach we investigate a homogeneous dilute weakly interacting Bose gas at finite temperature in vicinity of critical region. A longstanding debate, the shift of critical temperature, is considered and obtained in the universal form ΔTC/TC(0)=cn01/3asΔT_C/T_C^{(0)} = cn_0^{1/3}a_sΔTC​/TC(0)​=cn01/3​as​ with constants ccc and aaa. The non-condensate fraction is contributed by quantum fluctuations as well as thermal exitations and can be expressed in sum of three terms. These terms correspond to the quantum fluctuations, thermal fluctuations and both. Indeed, the specific heat capacity and critical exponents are calculated and in excellent agreement with those in previous works and experimental data.
Using a finite-temperature path integral Monte Carlo simulation (PIMC) method and finite-size scaling, we have investigated the interaction-induced shift of the phase-transition temperature for Bose-Einstein condensation of homogeneous weakly interacting Bose gases in three dimensions, which is given by a proposed analytical expression ${T}_{c}={T}_{c}^{0}{1+{c}_{1}a{n}^{1∕3}+[{c}_{2}^{\ensuremath{'}}\phantom{\rule{0.2em}{0ex}}\mathrm{ln}(a{n}^{1∕3})+{c}_{2}^{\ensuremath{''}}]{a}^{2}{n}^{2∕3}+\mathrm{O}({a}^{3}n)}$, where Tc0{T}_{c}^{0}Tc0​ is the critical temperature for an ideal gas, aaa is the sss-wave scattering length, and nnn is the number density. We have used smaller number densities and more time slices than in the previous PIMC simulations [Gruter et al., Phys. Rev. Lett. 79, 3549 (1997)] in order to understand the difference in the value of the coefficient c1{c}_{1}c1​ between their results and the (apparently) other reliable results in the literature. Our results show that ${({T}_{c}\ensuremath{-}{T}_{c}^{0})∕{T}_{c}^{0}}∕(a{n}^{1∕3})$ depends strongly on the interaction strength an1∕3a{n}^{1∕3}an1∕3 while the previous PIMC results are considerably flatter and smaller than our results. We obtain ${c}_{1}=1.32\ifmmode\pm\else\textpm\fi{}0.14$, in agreement with results from recent Monte Carlo methods of three-dimensional O(2) scalar ${\ensuremath{\phi}}^{4}$ field theory and variational perturbation theory.
We calculate the superfluid transition temperature of homogeneous interacting Bose gases in three and two spatial dimensions using large-scale path integral Monte Carlo simulations (with up to N=10;{5} particles). In 3D we investigate the limits of the universal critical behavior in terms of the scattering length alone by using different models for the interatomic potential. We find that this type of universality sets in at small values of the gas parameter na3 < or approximately 10(-4). This value is different from the estimate na3 < or approximately 10(-6) for the validity of the asymptotic expansion in the limit of vanishing na3. In 2D we study the Berezinskii-Kosterlitz-Thouless transition of a gas with hard-core interactions. For this system we find good agreement with the classical lattice |psi|4 model up to very large densities. We also explain the origin of the existing discrepancy between previous studies of the same problem.
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 compute the critical temperature T_c of a weakly interacting uniform Bose gas in the canonical ensemble, extending the criterion of condensation provided by the counting statistics for the uniform ideal gas. Using ordinary perturbation theory, we find in first order (Tc−Tc0)/Tc0=−0.93aρ1/3(T_c-T_c^0)/T_c^0 = -0.93 aρ^{1/3}(Tc​−Tc0​)/Tc0​=−0.93aρ1/3, where T_c^0 is the transition temperature of the corresponding ideal Bose gas, a is the scattering length, and ρρρ is the particle number density.