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Title: Transfer matrix spectrum for the finite-width Ising model with adjustable boundary conditions: Exact solution

Abstract

Using the spinor approach, the authors calculate exactly the complete spectrum of the transfer matrix for the finite-width, planar Ising model with adjustable boundary conditions. Specifically, in order to control the boundary conditions, they consider an Ising model wrapped around the cylinder, and introduce along the axis a seam of defect bonds of variable strength. Depending on the boundary conditions used, the mass gap is found to vanish algebraically or exponentially with the size of the system. These results are compared with recent numerical simulations, and with random-walk and capillary-wave arguments.

Authors:
; ;  [1]
  1. Clarkson Univ., Potsdam, NY (USA)
Publication Date:
OSTI Identifier:
6196550
Resource Type:
Journal Article
Journal Name:
Journal of Statistical Physics; (USA)
Additional Journal Information:
Journal Volume: 56:5-6; Journal ID: ISSN 0022-4715
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ISING MODEL; TRANSFER MATRIX METHOD; BOUNDARY CONDITIONS; COMPUTERIZED SIMULATION; CRYSTAL DEFECTS; CRYSTAL LATTICES; CYLINDERS; EIGENVALUES; EQUATIONS OF MOTION; MASS; MATRICES; NUMERICAL SOLUTION; ONSAGER RELATIONS; ORTHOGONAL TRANSFORMATIONS; PAULI SPIN OPERATORS; QUANTUM MECHANICS; ROTATION; SPECTRA; SPIN; SPINORS; STATISTICAL MECHANICS; THERMODYNAMICS; TRANSPORT THEORY; ANGULAR MOMENTUM; ANGULAR MOMENTUM OPERATORS; CRYSTAL MODELS; CRYSTAL STRUCTURE; DIFFERENTIAL EQUATIONS; EQUATIONS; MATHEMATICAL MODELS; MATHEMATICAL OPERATORS; MECHANICS; MOTION; PARTIAL DIFFERENTIAL EQUATIONS; PARTICLE PROPERTIES; QUANTUM OPERATORS; SIMULATION; TRANSFORMATIONS; 656002* - Condensed Matter Physics- General Techniques in Condensed Matter- (1987-); 657002 - Theoretical & Mathematical Physics- Classical & Quantum Mechanics

Citation Formats

Abraham, D B, Ko, L F, and Svrakic, N M. Transfer matrix spectrum for the finite-width Ising model with adjustable boundary conditions: Exact solution. United States: N. p., 1989. Web. doi:10.1007/BF01016767.
Abraham, D B, Ko, L F, & Svrakic, N M. Transfer matrix spectrum for the finite-width Ising model with adjustable boundary conditions: Exact solution. United States. https://doi.org/10.1007/BF01016767
Abraham, D B, Ko, L F, and Svrakic, N M. Fri . "Transfer matrix spectrum for the finite-width Ising model with adjustable boundary conditions: Exact solution". United States. https://doi.org/10.1007/BF01016767.
@article{osti_6196550,
title = {Transfer matrix spectrum for the finite-width Ising model with adjustable boundary conditions: Exact solution},
author = {Abraham, D B and Ko, L F and Svrakic, N M},
abstractNote = {Using the spinor approach, the authors calculate exactly the complete spectrum of the transfer matrix for the finite-width, planar Ising model with adjustable boundary conditions. Specifically, in order to control the boundary conditions, they consider an Ising model wrapped around the cylinder, and introduce along the axis a seam of defect bonds of variable strength. Depending on the boundary conditions used, the mass gap is found to vanish algebraically or exponentially with the size of the system. These results are compared with recent numerical simulations, and with random-walk and capillary-wave arguments.},
doi = {10.1007/BF01016767},
url = {https://www.osti.gov/biblio/6196550}, journal = {Journal of Statistical Physics; (USA)},
issn = {0022-4715},
number = ,
volume = 56:5-6,
place = {United States},
year = {1989},
month = {9}
}