scholarly journals A tree-decomposed transfer matrix for computing exact Potts model partition functions for arbitrary graphs, with applications to planar graph colourings

2010 ◽  
Vol 43 (38) ◽  
pp. 385001 ◽  
Author(s):  
Andrea Bedini ◽  
Jesper Lykke Jacobsen
Keyword(s):  
Planar Graph ◽  
Transfer Matrix ◽  
Potts Model ◽  
Partition Functions ◽  
Graph Colourings ◽  
Arbitrary Graphs

scholarly journals Character decomposition of Potts model partition functions, II: Toroidal geometry

2006 ◽  
Vol 750 (3) ◽  
pp. 229-249 ◽  
Author(s):  
Jean-François Richard ◽  
Jesper Lykke Jacobsen
Keyword(s):  
Potts Model ◽  
Partition Functions ◽  
Toroidal Geometry

Statement B and the Yang-Baxter Equation

2011 ◽  
Author(s):  
Ben Brubaker ◽  
Daniel Bump ◽  
Solomon Friedberg
Keyword(s):  
Statistical Mechanics ◽  
Dirichlet Series ◽  
Weyl Group ◽  
Transfer Matrix ◽  
Baxter Equation ◽  
Partition Functions ◽  
Alternate Proof ◽  
Crystal Basis ◽  
Exactly Solved Models ◽  
Multiple Dirichlet Series

This chapter reinterprets Statements A and B in a different context, and yet again directly proves that the reinterpreted Statement B implies the reinterpreted Statement A in Theorem 19.10. The p-parts of Weyl group multiple Dirichlet series, with their deformed Weyl denominators, may be expressed as partition functions of exactly solved models in statistical mechanics. The transition to ice-type models represents a subtle shift in emphasis from the crystal basis representation, and suggests the introduction of a new tool, the Yang-Baxter equation. This tool was developed to prove the commutativity of the row transfer matrix for the six-vertex and similar models. This is significant because Statement B can be formulated in terms of the commutativity of two row transfer matrices. This chapter presents an alternate proof of Statement B using the Yang-Baxter equation.

scholarly journals QUASI-PARTICLES IN THE CHIRAL POTTS MODEL

1994 ◽  
Vol 08 (25n26) ◽  
pp. 3601-3621 ◽  
Author(s):  
RINAT KEDEM ◽  
BARRY M. McCOY
Keyword(s):  
Transfer Matrix ◽  
Potts Model ◽  
Numerical Study ◽  
Particle Spectrum ◽  
Exact Results ◽  
Chiral Potts Model ◽  
Quasi Particle ◽  
Massive Phase ◽  
Matrix Eigenvalues ◽  
Potts Chain

We study the quasi-particle spectrum of the integrable three-state chiral Potts chain in the massive phase by combining a numerical study of the zeros of associated transfer matrix eigenvalues with the exact results of the ferromagnetic three-state Potts chain and the three-state superintegrable chiral Potts model. We find that the spectrum is described in terms of quasi-particles with momenta restricted only to segments of the Brillouin zone 0≤P≤2π where the boundaries of the segments depend on the chiral angles of the model.

scholarly journals FERMIONIC CHARACTER SUMS AND THE CORNER TRANSFER MATRIX

1994 ◽  
Vol 09 (07) ◽  
pp. 1115-1136 ◽  
Author(s):  
EZER MELZER
Keyword(s):  
Transfer Matrix ◽  
Series Representation ◽  
Partition Functions ◽  
Modular Invariant ◽  
Linear Dispersion ◽  
Quasi Particle ◽  
Conformal Field ◽  
Rsos Models ◽  
Lattice Limit ◽  
Virasoro Characters

We present a "natural finitization" of the fermionic q-series (certain generalizations of the Rogers–Ramanujan sums) which were recently conjectured to be equal to Virasoro characters of the unitary minimal conformal field theory (CFT) ℳ (p, p + 1). Within the quasi-particle interpretation of the fermionic q-series this finitization amounts to introducing an ultraviolet cutoff, which — contrary to a lattice spacing — does not modify the linear dispersion relation. The resulting polynomials are conjectured (proven, for p = 3, 4) to be equal to corner transfer matrix (CTM) sums which arise in the computation of order parameters in regime III of the r = p + 1 RSOS model of Andrews, Baxter and Forrester. Following Schur's proof of the Rogers–Ramanujan identities, these authors have shown that the infinite lattice limit of the CTM sums gives what later became known as the Rocha–Caridi formula for the Virasoro characters. Thus we provide a proof of the fermionic q-series representation for the Virasoro characters for p = 4 (the case p = 3 is "trivial"), in addition to extending the remarkable connection between CFT and off-critical RSOS models. We also discuss finitizations of the CFT modular-invariant partition functions.

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