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arXiv · 1407.2014

Stochastic processes with Z_N symmetry and complex Virasoro representations. The partition functions

Francisco C. Alcaraz·Pavel Pyatov·Vladimir Rittenberg
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Abstract

In a previous Letter (J. Phys. A v.47 (2014) 212003) we have presented numerical evidence that a Hamiltonian expressed in terms of the generators of the periodic Temperley-Lieb algebra has, in the finite-size scaling limit, a spectrum given by representations of the Virasoro algebra with complex highest weights. This Hamiltonian defines a stochastic process with a Z_N symmetry. We give here analytical expressions for the partition functions for this system which confirm the numerics. For N even, the Hamiltonian has a symmetry which makes the spectrum doubly degenerate leading to two independent stochastic processes. The existence of a complex spectrum leads to an oscillating approach to the stationary state. This phenomenon is illustrated by an example.

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Francisco C. Alcaraz, Pavel Pyatov, Vladimir Rittenberg. 2014-07-08. Stochastic processes with Z_N symmetry and complex Virasoro representations. The partition functions. https://doi.org/10.1088/1751-8113/47/46/462001

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