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

American Journal of Physics

Thermodynamic properties of an anharmonic fermionic oscillator

S. M. de Souza, S. Moss de Oliveira, M. T. Thomaz

Published Dec 1, 1992• 4 citations
Publisher

Abstract

An exactly soluble fermionic system (anharmonic oscillator) is presented. Exact expressions for average quantities such as the number of particles, energy, and magnetization of an ensemble of quantum systems in equilibrium with a reservoir of particles and heat are derived. Critical curves of the average magnetization as a function of temperature are obtained for a lattice of interacting anharmonic oscillators within the mean field approximation. To clarify the role played by the parameters of the present model, the Ising model is studied as a limiting case.

DOI
10.1119/1.16958

Related papers

A soluble one dimensional model of an interacting Fermi gas. I

Eleonora M. Witteles, Gideon Carmi

The authors study a one dimensional model system of fermions which proves to be exactly soluble in the thermodynamic limit. It is shown that the thermodynamic functions for the model system are the same as for a system of noninteracting fermions in a harmonic oscillator well. As a special case of the model system, with a particular choice for the coupling constant, it reduces to a particular two-species system of fermions interacting via pairwise harmonic forces. For this case of the two-species system the free energy per particle, the pressure the specific heat at constant volume, and the isothermal compressibility are calculated in the canonical ensemble in closed form. It is shown that this system does not undergo a phase transition.

Journal of physics. A, Proceedings of the Physical Society. General•May 1, 1972•1 citation

Grassmann algebra and fermions in the lattice: A simple example

S. M. de Souza, M. T. Thomaz

Using the exact results for integrals of exponentials of polynomials of Grassmann variables and the Feynman construction of path integrals, an approximate method is presented to calculate the thermodynamic quantities of a fermionic system in equilibrium with a reservoir at temperature T and chemical potential μ. To exemplify, the quantum anharmonic fermionic oscillator is considered in a lattice with N points, where N=2, 3, and 4.

Journal of Mathematical Physics•Dec 1, 1991•4 citations

Phase properties of the mean-field Ising model with three-spin interaction

Godwin Osabutey

The equilibrium and phase properties of the Ising model with three-spin interaction and an external field are studied within the framework of mean-field approximation. The thermodynamic properties of the model reveals two coexistence curves, signifying two distinct second-order phase transitions, dependent on the domain of the interaction parameter. The critical exponents of the magnetic order parameter are calculated in all directions of the phase space and show their agreement with the mean-field universality class.

Journal of Mathematical Physics•Jun 1, 2024•5 citations

Low temperature thermodynamic properties of a polarized Fermi gas in a quartic trap

Mark J. DelloStritto, Theja N. De Silva

We study low temperature thermodynamic properties of a polarized Fermi gas trapped in a quartic anharmonic potential. We use a semi classical approximation and a low temperature series expansion method to derive analytical expressions for various thermodynamic quantities. These quantities include the total energy, particle number, and heat capacity for both positive and negative anharmonic confinements.

arXiv:1009.3953•Sep 20, 2010•0 citations

Exact thermal properties of free-fermionic spin chains

Michał Białończyk, Fernando Gómez-Ruiz, Adolfo del Campo

An exact description of integrable spin chains at finite temperature is provided using an elementary algebraic approach in the complete Hilbert space of the system. We focus on spin chain models that admit a description in terms of free fermions, including paradigmatic examples such as the one-dimensional transverse-field quantum Ising and XY models. The exact partition function is derived and compared with the ubiquitous approximation in which only the positive parity sector of the energy spectrum is considered. Errors stemming from this approximation are identified in the neighborhood of the critical point at low temperatures. We further provide the full counting statistics of a wide class of observables at thermal equilibrium and characterize in detail the thermal distribution of the kink number and transverse magnetization in the transverse-field quantum Ising chain.

arXiv:2103.16322•SciPost Physics•Jul 15, 2021•11 citations

QUANTUM EFFECTS IN AN ANHARMONIC CRYSTAL

Kozitsky

A model of quantum particles performing D -dimensional anharmonic oscillations around their equilibrium positions which form the d -dimensional simple cubic lattice Zd is considered. The model undergoes a structural phase transition when the fluctuations of displacements of particles become macroscopic. This phenomenon is described by susceptibilities depending on Matsubara frequencies ωn , n ∈ Z . We prove two theorems concerning the thermodynamic limits of these susceptibilities. The first theorem states that the susceptibilities with nonzero ωn remain bounded at all temperatures, which means that the macroscopic fluctuations in the model are always non-quantum. The second theorem gives a sufficient condition for the static susceptibility (i.e. corresponding to ωn = 0 ) to be bounded at all temperatures. This condition involves the particle mass, the anharmonicity parameters and the interaction intensity. The physical meaning of this result is that, for all D and all values of the temperature, strong quantum effects suppress critical points and the long range order. The proof is performed in the approach where the susceptibilities are represented as functional integrals. A brief description of the main features of this approach is delivered.

Condensed Matter Physics•Jan 1, 2002•2 citations
An exactly soluble fermionic system (anharmonic oscillator) is presented. Exact expressions for average quantities such as the number of particles, energy, and magnetization of an ensemble of quantum systems in equilibrium with a reservoir of particles and heat are derived. Critical curves of the average magnetization as a function of temperature are obtained for a lattice of interacting anharmonic oscillators within the mean field approximation. To clarify the role played by the parameters of the present model, the Ising model is studied as a limiting case.
The authors study a one dimensional model system of fermions which proves to be exactly soluble in the thermodynamic limit. It is shown that the thermodynamic functions for the model system are the same as for a system of noninteracting fermions in a harmonic oscillator well. As a special case of the model system, with a particular choice for the coupling constant, it reduces to a particular two-species system of fermions interacting via pairwise harmonic forces. For this case of the two-species system the free energy per particle, the pressure the specific heat at constant volume, and the isothermal compressibility are calculated in the canonical ensemble in closed form. It is shown that this system does not undergo a phase transition.
The equilibrium and phase properties of the Ising model with three-spin interaction and an external field are studied within the framework of mean-field approximation. The thermodynamic properties of the model reveals two coexistence curves, signifying two distinct second-order phase transitions, dependent on the domain of the interaction parameter. The critical exponents of the magnetic order parameter are calculated in all directions of the phase space and show their agreement with the mean-field universality class.
An exact description of integrable spin chains at finite temperature is provided using an elementary algebraic approach in the complete Hilbert space of the system. We focus on spin chain models that admit a description in terms of free fermions, including paradigmatic examples such as the one-dimensional transverse-field quantum Ising and XY models. The exact partition function is derived and compared with the ubiquitous approximation in which only the positive parity sector of the energy spectrum is considered. Errors stemming from this approximation are identified in the neighborhood of the critical point at low temperatures. We further provide the full counting statistics of a wide class of observables at thermal equilibrium and characterize in detail the thermal distribution of the kink number and transverse magnetization in the transverse-field quantum Ising chain.
A model of quantum particles performing D -dimensional anharmonic oscillations around their equilibrium positions which form the d -dimensional simple cubic lattice Zd is considered. The model undergoes a structural phase transition when the fluctuations of displacements of particles become macroscopic. This phenomenon is described by susceptibilities depending on Matsubara frequencies ωn , n ∈ Z . We prove two theorems concerning the thermodynamic limits of these susceptibilities. The first theorem states that the susceptibilities with nonzero ωn remain bounded at all temperatures, which means that the macroscopic fluctuations in the model are always non-quantum. The second theorem gives a sufficient condition for the static susceptibility (i.e. corresponding to ωn = 0 ) to be bounded at all temperatures. This condition involves the particle mass, the anharmonicity parameters and the interaction intensity. The physical meaning of this result is that, for all D and all values of the temperature, strong quantum effects suppress critical points and the long range order. The proof is performed in the approach where the susceptibilities are represented as functional integrals. A brief description of the main features of this approach is delivered.