PMID: 11909161Mar 23, 2002Paper

Exact amplitude ratio and finite-size corrections for the MxN square lattice Ising model

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Nickolay Izmailian, Chin-Kun Hu

Abstract

Let f, U, and C represent, respectively, the free energy, the internal energy, and the specific heat of the critical Ising model on the MxN square lattice with periodic boundary conditions, and f(infinity) represents f for fixed M/N and N-->infinity. We find that f, U, and C can be written as N(f-f(infinity))= summation operator(infinity)(i=1)f(2i-1)/N(2i-1), U=-square root of [2]+ summation operator(infinity)(i=1)u(2i-1)/N(2i-1), and C=8 ln N/pi+ summation operator(infinity)(i=0)c(i)/N(i), i.e., Nf and U are odd functions of N(-1). We also find that u(2i-1)/c(2i-1)=1/square root of [2] and u(2i)/c(2i)=0 for 1 < or = i <infinity and obtain closed form expressions for f, U, and C up to orders 1/N(5), 1/N(5), and 1/N(3), respectively, which implies an analytic equation for c(5).

References

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Citations

May 17, 2012·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·A MalakisG Aslan
Sep 28, 2010·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh Izmailian, Ming-Chang Huang
Mar 15, 2015·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh Izmailian, R Kenna
Oct 26, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh IzmailianChin-Kun Hu
Jun 13, 2002·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh IzmailianChin-Kun Hu
Nov 13, 2007·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh Izmailian, Chin-Kun Hu
Feb 21, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh IzmailianChin-Kun Hu
Feb 21, 2006·Physical Review Letters·N Sh IzmailianChin-Kun Hu
Jul 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·I Lyberg
Feb 16, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh Izmailian, Chin-Kun Hu
Sep 21, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh Izmailian, Ralph Kenna
Nov 13, 2008·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hiroshi Watanabe, Chin-Kun Hu
Mar 19, 2013·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Hon Wai Lau, Peter Grassberger
May 23, 2006·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ming-Chya Wu
Dec 21, 2011·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·N Sh Izmailian
Oct 26, 2005·Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics·Ming-Chya WuN Sh Izmailian

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