Triangular Potts model at its transition temperature, and related models

1978 ◽  
Vol 358 (1695) ◽  
pp. 535-559 ◽  
Keyword(s):  
Free Energy ◽  
Transition Temperature ◽  
Internal Energy ◽  
Potts Model ◽  
Triangular Lattice ◽  
Operator Method ◽  
Type Model ◽  
Bond Percolation ◽  
Vertex Model ◽  
Percolation Problem

Kelland has solved a restricted ice-type model on the triangular lattice. Here it is shown that this is equivalent to a restricted six-vertex model on the Kagomé lattice, and to the g-state triangular (or hexagonal) Potts model at its transition temperature T c . This enables us to obtain the free energy, internal energy and latent heat of the Potts model at T c . The relation of this work to the operator method of Temperley and Lieb is explained, and this method is used to consider a generalized triangular Potts model which includes a three-site interaction on alternate triangles. It is shown that this model is self-dual. The results for the bond percolation problem on the triangular lattice give an excellent verification of series expansion predictions.

Critical antiferromagnetic square-lattice Potts model

1982 ◽  
Vol 383 (1784) ◽  
pp. 43-54 ◽  
Keyword(s):  
Free Energy ◽  
Critical Temperature ◽  
Internal Energy ◽  
Latent Heat ◽  
Potts Model ◽  
Square Lattice ◽  
Isotropic Model ◽  
First Order

The critical temperature of the antiferromagnetic q -state Potts model on the square lattice is located, and the critical free energy and internal energy are evaluated. As with the ferromagnetic model, the transition is continuous for q ≼4, and its first-order (i. e. has latent heat) for q >4. However, only for q ≼3 can the critical temperature be real. For the isotropic model the criticality condition is exp( J / k T ) = -1 + (4- q ) ½ .

First and second laws of thermodynamics: relationship, “inconsistency”, hidden effects

2020 ◽  
pp. 63-73
Author(s):  
A. M. Savchenko ◽  
Yu. V. Konovalov ◽  
A. V. Laushkin
Keyword(s):  
Free Energy ◽  
Internal Energy ◽  
Second Law Of Thermodynamics ◽  
Second Law ◽  
Entropy Of Mixing ◽  
Ideal Mixing ◽  
Laws Of Thermodynamics ◽  
Relationship Of ◽  
The Relationship

The relationship of the first and second laws of thermodynamics based on their energy nature is considered. It is noted that the processes described by the second law of thermodynamics often take place hidden within the system, which makes it difficult to detect them. Nevertheless, even with ideal mixing, an increase in the internal energy of the system occurs, numerically equal to an increase in free energy. The largest contribution to the change in the value of free energy is made by the entropy of mixing, which has energy significance. The entropy of mixing can do the job, which is confirmed in particular by osmotic processes.

Studies in the Vulcanization of Rubber. I—Thermochemistry of Vulcanization of Rubber

1930 ◽  
Vol 3 (4) ◽  
pp. 631-639
Author(s):  
John T. Blake
Keyword(s):  
Free Energy ◽  
Internal Energy ◽  
Chemical Reaction ◽  
Effect Of Temperature ◽  
Heat Of Reaction ◽  
Chemical Affinity ◽  
Direct Measure ◽  
Total Change

Abstract WHEN a chemical reaction takes place, it is usually accompanied by an absorption or evolution of heat. The amount of the heat interchange is not a direct measure of the chemical affinity involved in the reaction, nor is it a measure of the free energy of the reaction. The heat of reaction, however, is a measure of the total change in internal energy and is of importance, therefore, in calculating the effect of temperature on a reaction and in elucidating the mechanism of it.

INTEGRABLE FIELD THEORY OF THE q-STATE POTTS MODEL WITH 0

1992 ◽  
Vol 07 (21) ◽  
pp. 5317-5335 ◽  
Author(s):  
LEUNG CHIM ◽  
ALEXANDER ZAMOLODCHIKOV
Keyword(s):  
Field Theory ◽  
Potts Model ◽  
Density Operator ◽  
Size Distributions ◽  
Quantum Field ◽  
Particle Content ◽  
Integrable Field Theory ◽  
Percolation Problem ◽  
S Matrix ◽  
Integrable Field

Two-dimensional quantum field theory obtained by perturbing the q-state Potts-model CFT (0<q<4) with the energy-density operator Φ(2, 1) is shown to be integrable. The particle content of this QFT is conjectured and the factorizable S matrix is proposed. The limit q→1 is related to the isotropic-percolation problem in 2D and so we make a few predictions about the size distributions of the percolating clusters in the scaling domain.

scholarly journals QUANTUM GROUP APPROACH TO A SOLUBLE VERTEX MODEL WITH GENERALIZED ICE RULE

1996 ◽  
Vol 11 (10) ◽  
pp. 1747-1761
Author(s):  
C.L. SOW ◽  
T.T. TRUONG
Keyword(s):  
Free Energy ◽  
Quantum Mechanics ◽  
Positive Integer ◽  
Quantum Group ◽  
Algebraic Structure ◽  
Square Lattice ◽  
Free Fermion ◽  
Vertex Model ◽  
Group Approach ◽  
Operator Structure

Using the representation of the quantum group SL q(2) by the Weyl operators of the canonical commutation relations in quantum mechanics, we construct and solve a new vertex model on a square lattice. Random variables on horizontal bonds are Ising variables, and those on the vertical bonds take half positive integer values. The vertex is subjected to a generalized form of the so-called “ice rule,” its property is studied in detail and its free energy calculated with the method of quantum inverse scattering. Remarkably, in analogy with the usual six-vertex model, there exists a “free-fermion” limit with a novel rich operator structure. The existing algebraic structure suggests a possible connection with a lattice neutral plasma of charges, via the fermion-boson correspondence.

scholarly journals Free energy versus internal energy potential for heavy quark systems at finite temperature

2014 ◽  
Vol 931 ◽  
pp. 607-611
Author(s):  
Taesoo Song ◽  
Su Houng Lee ◽  
Kenji Morita ◽  
Che Ming Ko
Keyword(s):  
Free Energy ◽  
Heavy Quark ◽  
Internal Energy ◽  
Finite Temperature ◽  
Energy Potential

THERMODYNAMICS OF SOME SPECIAL FIELDS

1953 ◽  
Vol 31 (2) ◽  
pp. 329-336
Author(s):  
R. V. Krotkov ◽  
A. E. Scheidegger
Keyword(s):  
Free Energy ◽  
Electromagnetic Field ◽  
Internal Energy ◽  
Thermodynamic Functions ◽  
External Electromagnetic Field ◽  
Explicit Formulas ◽  
First Case ◽  
Quantized Fields

The free energy, internal energy, and entropy of two quantized fields are calculated, using the method introduced by Scheidegger and McKay. The two fields examined are those representing (a) an ensemble of mesons bound by an interaction with their source (a nucleon), and (b) an ensemble of electrons perturbed by an external electromagnetic field. The presence of a source in the first case is found to have no effect on the thermodynamic functions of the mesons, while an external electromagnetic field does affect the thermodynamic functions of the electrons. Explicit formulas in the latter case are given.

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