The Ising chain constrained to an even or odd number of positive spins

We investigate the statistical mechanics of the periodic one-dimensional Ising chain when the number of positive spins is constrained to be either an even or an odd number. We calculate the partition function using a generalization of the transfer matrix method. On this basis, we derive the exact ma...

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Bibliographic Details
Published inJournal of statistical mechanics Vol. 2015; no. 3; pp. P03004 - 24
Main Author Gastner, Michael T
Format Journal Article
LanguageEnglish
Published IOP Publishing and SISSA 03.03.2015
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Summary:We investigate the statistical mechanics of the periodic one-dimensional Ising chain when the number of positive spins is constrained to be either an even or an odd number. We calculate the partition function using a generalization of the transfer matrix method. On this basis, we derive the exact magnetization, susceptibility, internal energy, heat capacity and correlation function. We show that in general the constraints substantially slow down convergence to the thermodynamic limit. By taking the thermodynamic limit together with the limit of zero temperature and zero magnetic field, the constraints lead to new scaling functions and different probability distributions for the magnetization. We demonstrate how these results solve a stochastic version of the one-dimensional voter model.
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ISSN:1742-5468
1742-5468
DOI:10.1088/1742-5468/2015/03/P03004