THE INHOMOGENEOUS HEISENBERG CHAIN WITH THE INTERACTION OF CLASSICAL AND QUANTUM SPINS

2000 ◽  
Vol 14 (11) ◽  
pp. 1179-1185
Author(s):  
B. I. SADOVNIKOV ◽  
N. G. INOZEMTSEVA ◽  
V. I. INOZEMTSEV
Keyword(s):  
Free Energy ◽  
Specific Heat ◽  
Heisenberg Chain ◽  
Spin Correlations ◽  
Quantum Spins ◽  
Explicit Expressions

The thermodynamics of an inhomogeneous 1D Heisenberg chain with alternating classical and quantum spins is studied. The explicit expressions for the free energy, specific heat, thermal spin correlations and linear susceptibility are found.

scholarly journals T − W relation and free energy of the Heisenberg chain at a finite temperature

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Pengcheng Lu ◽  
Yi Qiao ◽  
Junpeng Cao ◽  
Wen-Li Yang ◽  
Kang jie Shi ◽  
...  
Keyword(s):  
Free Energy ◽  
Spin Chain ◽  
Quantum Spin ◽  
Heisenberg Chain ◽  
Quantum Spin Chain ◽  
Heisenberg Spin ◽  
Heisenberg Spin Chain ◽  
Lattice Quantum ◽  
Quantum Integrable Models ◽  
Invariant Quantum

Abstract A new nonlinear integral equation (NLIE) describing the thermodynamics of the Heisenberg spin chain is derived based on the t − W relation of the quantum transfer matrices. The free energy of the system in a magnetic field is thus obtained by solving the NLIE. This method can be generalized to other lattice quantum integrable models. Taking the SU(3)-invariant quantum spin chain as an example, we construct the corre- sponding NLIEs and compute the free energy. The present results coincide exactly with those obtained via other methods previously.

scholarly journals Anharmonic Contributions to the Vibratory Free Energy of a Lattice

1964 ◽  
Vol 17 (3) ◽  
pp. 269 ◽  
Author(s):  
P Lloyd
Keyword(s):  
Free Energy ◽  
Specific Heat ◽  
Constant Volume ◽  
Bethe Approximation ◽  
Rate Of Increase

The anharmonic contribution to the free energy of a lattice is evaluated by means of a Bethe approximation. The approximation is accurate to within 3% for the model valuated by Maradudin, Flinn, and Coldwell� Horsfall. The anharmonic contribution to the specific heat at constant volume of a model of sodium is evaluated.The specific heat is found to increase as the temperature rises but the rate of increase is lower than the observed value

Specific Heat of the Spin-1/2 Antiferromagnetic Heisenberg Chain

2001 ◽  
Vol 18 (9) ◽  
pp. 1261-1263 ◽  
Author(s):  
Yun Guo-Hong ◽  
Liang Xi-Xia
Keyword(s):  
Specific Heat ◽  
Heisenberg Chain

scholarly journals Voros coefficients for the hypergeometric differential equations and Eynard–Orantin’s topological recursion: Part II: For confluent family of hypergeometric equations

2019 ◽  
Vol 4 (1) ◽  
Author(s):  
Kohei Iwaki ◽  
Tatsuya Koike ◽  
Yumiko Takei
Keyword(s):  
Free Energy ◽  
Differential Equations ◽  
Classical Limit ◽  
Bernoulli Polynomials ◽  
Bernoulli Numbers ◽  
Spectral Curves ◽  
Topological Recursion ◽  
Hypergeometric Equations ◽  
Explicit Expressions

Abstract We show that each member of the confluent family of the Gauss hypergeometric equations is realized as quantum curves for appropriate spectral curves. As an application, relations between the Voros coefficients of those equations and the free energy of their classical limit computed by the topological recursion are established. We will also find explicit expressions of the free energy and the Voros coefficients in terms of the Bernoulli numbers and Bernoulli polynomials. Communicated by: Youjin Zhang

ISING MODEL IN THE MAGNETIC FIELD iπkT/2

1988 ◽  
Vol 02 (03n04) ◽  
pp. 471-481 ◽  
Author(s):  
K. Y. LIN ◽  
F. Y. WU
Keyword(s):  
Magnetic Field ◽  
Free Energy ◽  
Ising Model ◽  
Zero Field ◽  
Two Dimensional ◽  
Anisotropic Interactions ◽  
The Magnetic Field ◽  
Explicit Expressions

It is shown that the free energy and the magnetization of an Ising model in the magnetic field H = iπkT/2 can be obtained directly from corresponding expressions of these quantities in zero field, provided that the latter are known for sufficiently anisotropic interactions. Using this approach we derive explicit expressions of the free energy and the magnetization at H = iπkT/2 for a number of two-dimensional lattices.

Schemes for the calculation of the free energy and specific heat for marginal Fermi liquids in the normal and superconducting phase

1995 ◽  
Vol 73 (7-8) ◽  
pp. 497-504 ◽  
Author(s):  
Ranjan Chaudhury
Keyword(s):  
Free Energy ◽  
Specific Heat ◽  
Fermi Liquid ◽  
Superconducting Phase ◽  
Fermi Liquids ◽  
Many Body ◽  
Boson Exchange ◽  
Marginal Fermi Liquid

Several schemes based on the fermionic many-body approach and the boson-exchange approach are developed to calculate the free energy and specific heat for a marginal Fermi liquid in the normal and superconducting phase. The merits and demerits of these schemes are analyzed and compared. The origin of the failure of the simple Bardeen–Stephen formula is also highlighted. The analysis is carried out in light of some experiments.

Thermodynamics of The Pd43Ni10Cu27P20 Bulk Metallic Glass Forming Alloy

2003 ◽  
Vol 806 ◽  
Author(s):  
Masahiro Kuno ◽  
Ludi A. Shadowspeaker ◽  
Jan Schroers ◽  
Ralf Busch
Keyword(s):  
Heat Capacity ◽  
Free Energy ◽  
Metallic Glass ◽  
Specific Heat ◽  
Bulk Metallic Glass ◽  
Gibbs Free Energy ◽  
Specific Heat Capacity ◽  
Undercooled Liquid ◽  
Glass Forming ◽  
Crystalline Mixture

ABSTRACTThe thermodynamics of the bulk metallic glass forming Pd43Ni10Cu27P20 alloy were investigated with differential scanning calorimetry (DSC). The specific heat capacity of the undercooled liquid with respect to the crystalline mixture was measured in the DSC simultaneously with the enthalpy of crystallization over the entire supercooled liquid region. The enthalpy, entropy, and Gibbs free energy change between the liquid and the crystalline mixture was determined from the specific heat capacity data. The calculated enthalpy function closely matched the enthalpies of crystallization that were measured in the DSC, which verifies the validity of the thermodynamic model used. A small Gibbs free energy difference between undercooled liquid and crystalline mixture was found for decreasing temperature in Pd43Ni10Cu27P20 when compared to other glass forming alloys. This reflects a small driving force for crystallization when undercooling this alloy and is the main contributing factor for its high glass forming ability.

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