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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Published in | Journal of statistical mechanics Vol. 2015; no. 3; pp. P03004 - 24 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
IOP Publishing and SISSA
03.03.2015
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Subjects | |
Online Access | Get full text |
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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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Bibliography: | ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 1742-5468 1742-5468 |
DOI: | 10.1088/1742-5468/2015/03/P03004 |