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Modern Physics Letters B

EXACT BOUNDARY MAGNETIZATION OF THE LAYERED ISING MODEL ON TRIANGULAR AND HONEYCOMB LATTICES

Alessandro Pelizzola

Published Feb 28, 1996• 2 citations
Publisher

Abstract

In the present paper we extend a previous exact calculation of the boundary magnetization of the square lattice layered Ising model, based on a transfer-matrix effective-field technique, to the triangular lattice. The result is then further extended to the honeycomb lattice by means of a star-triangle transformation. Finally, the (11) boundary of the square lattice is analyzed as a particular case of the triangular and honeycomb lattices.

DOI
10.1142/s0217984996000171

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In the present paper we extend a previous exact calculation of the boundary magnetization of the square lattice layered Ising model, based on a transfer-matrix effective-field technique, to the triangular lattice. The result is then further extended to the honeycomb lattice by means of a star-triangle transformation. Finally, the (11) boundary of the square lattice is analyzed as a particular case of the triangular and honeycomb lattices.
Transfer matrix methods are used to locate accurate phase boundary of the triangular lattice antiferromagnetic Ising model in magnetic field. Universal quantities such as the central charge and the first few scaling dimensions are obtained along the phase boundary except near the zero field point where the crossover effect degrades convergence. Numerical results are fully consistent with the operator content of the 3-state Potts model indicating that whole phase boundary belongs to the 3-state Potts universality class.
The "star-triangle" and "decoration" transformations are generalized so as to apply to arbitrary mechanical systems coupled to the spins of a standard Ising net. This leads to exact solutions for further plane Ising nets and also for lattices in which the spins on alternate sites have a magnitude greater than S=12S=\frac{1}{2}S=21​. A general class of antiferromagnetic Ising models is constructed; exact closed expressions can be derived for all the thermodynamic and magnetic properties of these models in an arbitrary magnetic field.The magnetizations and susceptibilities of Ising nets in which different spins have different magnetic moments are investigated and a valuable relation between the susceptibilities of the honeycomb and triangular lattices is derived. It is shown how correlation functions involving a given spin can be expressed in terms of correlations involving the nearest-neighbor spins instead.