Lattice Models in Statistical Mechanics and Soliton Equations

1993 ◽  
pp. 418-440
Author(s):  
B. M. McCoy
Keyword(s):  
Statistical Mechanics ◽  
Lattice Models ◽  
Soliton Equations

A Hierarchy of Lattice Soliton Equations Associated with a New Discrete Eigenvalue Problem and Darboux Transformations

2015 ◽  
Vol 16 (7-8) ◽  
pp. 301-306 ◽  
Author(s):  
Ning Zhang ◽  
Tiecheng Xia
Keyword(s):  
Eigenvalue Problem ◽  
Exact Solutions ◽  
Spectral Parameter ◽  
Darboux Transformation ◽  
Lattice Models ◽  
Darboux Transformations ◽  
Discrete Eigenvalue ◽  
Negative Power ◽  
Soliton Equations ◽  
Gauge Transformations

AbstractBy considering a new discrete isospectral eigenvalue problem, a hierarchy of integrable positive and negative lattice models is derived. It is shown that they correspond to positive and negative power expansions of Lax operators with respect to the spectral parameter, respectively. And the equation in the resulting hierarchy is integrable in Liouville sense. Further, a Darboux transformation is established for the typical equations by using gauge transformations of Lax pairs, from which the exact solutions are given.

scholarly journals Some Algebraic Techniques for obtaining Low-temperature Series Expansions

1978 ◽  
Vol 31 (6) ◽  
pp. 515 ◽  
Author(s):  
IG Enting
Keyword(s):  
Low Temperature ◽  
Statistical Mechanics ◽  
Series Expansion ◽  
General Result ◽  
Generating Functions ◽  
Finite Lattice ◽  
Lattice Models ◽  
Temperature Series ◽  
Series Expansions ◽  
Lattice Method

It is shown that low-temperature series expansions for lattice models in statistical mechanics can be obtained from a consideration of only connected strong subgraphs of the lattice. This general result is used as the basis of a linked-cluster form of the method of partial generating functions and also as the basis for extending the finite lattice method of series expansion to low-temperature series.

Self-averaging in the statistical mechanics of some lattice models

2002 ◽  
Vol 35 (19) ◽  
pp. 4219-4227 ◽  
Author(s):  
E Orlandini ◽  
M C Tesi ◽  
S G Whittington
Keyword(s):  
Statistical Mechanics ◽  
Lattice Models

DISORDERED GROUND STATES OF CLASSICAL LATTICE MODELS

1991 ◽  
Vol 03 (02) ◽  
pp. 125-135 ◽  
Author(s):  
CHARLES RADIN
Keyword(s):  
Dynamical Systems ◽  
Statistical Mechanics ◽  
Continuous Spectrum ◽  
Ground State ◽  
Short Range ◽  
Ground States ◽  
Lattice Models ◽  
Positive Entropy ◽  
Classical Lattice ◽  
Classical Statistical Mechanics

We use strictly ergodic dynamical systems to describe two methods for constructing short range interactions of classical statistical mechanics models with unique ground states and unusual properties of disorder; in particular, these ground states can be mixing under translations (and therefore have purely continuous spectrum), and can have positive entropy. Because of the uniqueness of the ground state the disorder is not of the usual type associated with local degeneracy.

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