Disordered ground states for classical discrete-state problems in one dimension |
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Authors: | Geoff Canright Greg Watson |
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Institution: | (1) Department of Physics and Astronomy, University of Tennessee, 37996 Knoxville, Tennessee;(2) Solid State Division, Oak Ridge National Laboratory, 37831 Oak Ridge, Tennessee;(3) Rutherford Appleton Laboratory, Chilton, OX11 0QX Didcot, Oxon, UK |
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Abstract: | It is known that one-dimensional lattice problems with a discrete, finite set of states per site generically have periodic ground states (GSs). We consider slightly less generic cases, in which the Hamiltonian is constrained by either spin (S) or spatial (I) inversion symmetry (or both). We show that such constraints give rise to the possibility ofdisordered GSs over a finite fraction of the coupling-parameter space—that is, without invoking any nongeneric fine tuning of coupling constants, beyond that arising from symmetry. We find that such disordered GSs can arise for many values of the number of statesk at each site and the ranger of the interaction. The Ising (k=2) case is the least prone to disorder:I symmetry allows for disordered GSs (without fine tuning) only forr5, whileS symmetry never gives rise to disordered GSs. |
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Keywords: | Ising models disorder ground states directed graphs polytypes third law |
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