scholarly journals Domino tilings and the six-vertex model at its free-fermion point

2006 ◽  
Vol 39 (33) ◽  
pp. 10297-10306 ◽  
Author(s):  
Patrik L Ferrari ◽  
Herbert Spohn
Keyword(s):  
Free Fermion ◽  
Vertex Model ◽  
Domino Tilings

scholarly journals Arctic Curve of the Free-Fermion Six-Vertex Model in an L-Shaped Domain

2018 ◽  
Vol 174 (1) ◽  
pp. 1-27 ◽  
Author(s):  
F. Colomo ◽  
A. G. Pronko ◽  
A. Sportiello
Keyword(s):  
Free Fermion ◽  
Vertex Model ◽  
Arctic Curve ◽  
Shaped 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 Izergin-Korepin Analysis on the Projected Wavefunctions of the Generalized Free-Fermion Model

2017 ◽  
Vol 2017 ◽  
pp. 1-11 ◽  
Author(s):  
Kohei Motegi
Keyword(s):  
Symmetric Functions ◽  
Schur Functions ◽  
Free Fermion ◽  
Vertex Model ◽  
Fermion Model ◽  
Free Fermion Model

We apply the Izergin-Korepin analysis to the study of the projected wavefunctions of the generalized free-fermion model. We introduce a generalization of the L-operator of the six-vertex model by Bump-Brubaker-Friedberg and Bump-McNamara-Nakasuji. We make the Izergin-Korepin analysis to characterize the projected wavefunctions and show that they can be expressed as a product of factors and certain symmetric functions which generalizes the factorial Schur functions. This result can be seen as a generalization of the Tokuyama formula for the factorial Schur functions.

Conformal Symmetry in a Six-Vertex Model

1997 ◽  
Vol 12 (08) ◽  
pp. 1531-1550
Author(s):  
Q. Ho-Kim ◽  
T. T. Truong
Keyword(s):  
Conformal Symmetry ◽  
Virasoro Algebra ◽  
Explicit Construction ◽  
Complete Integrability ◽  
General Idea ◽  
Fermion Field ◽  
Free Fermion ◽  
Vertex Model ◽  
Virasoro Symmetry ◽  
Lattice Fermion

The concept of lattice Virasoro symmetry in completely integrable models of statistical mechanics is discussed in parallel with the notion of lattice Poincaré symmetry. To illustrate the general idea, we make an explicit construction of the full Virasoro algebra in terms of the lattice fermion field of the free-fermion six-vertex model in an external noncritical field. The conserved charges that characterize complete integrability are similarly obtained.

scholarly journals Yang–Baxter solution of dimers as a free-fermion six-vertex model

2017 ◽  
Vol 50 (43) ◽  
pp. 434001 ◽  
Author(s):  
Paul A Pearce ◽  
Alessandra Vittorini-Orgeas
Keyword(s):  
Free Fermion ◽  
Vertex Model
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