The residual entropy for a class of one-dimensional classical lattice models

Slegers, L.

doi:10.1088/0305-4470/21/17/017

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2016

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“…The importance of this phenomenon is due to the fact that it violates the third law of thermodynamics in the sense that the entropy of the system must vanish at the zero absolute temperature. The occurrence of such a phenomenon, in spin systems particularly [4][5][6][7][8], led to some authors reexamining such a basic principle [9][10][11]. Nowadays it is accepted that a thermodynamical system can have a non-zero entropy at zero absolute temperature, which is referred to as residual entropy [11].…”

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confidence: 99%

Degenerated ground-states in a spin chain with pair interactions: a characterization by symbolic dynamics

Corona

Salgado-García

2016

J. Stat. Mech.

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In this note we study a class of one-dimensional Ising chain having a highly degenerated set of ground-state configurations. The model consists of spin chain having infinite-range pair interactions with a given structure. We show that the set of ground-state configurations of such a model can be fully characterized by means of symbolic dynamics. Particularly we found that the set groundstate configurations defines what in symbolic dynamics is called sofic shift space. Finally we prove that this system has a non-vanishing residual entropy (the topological entropy of the shift space), which can be exactly calculated.

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