SciPost Phys. 8, 074 (2020) ·
published 8 May 2020

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We examine how systems in nonequilibrium steady states close to a continuous phase transition can still be described by a Landau potential if one forgoes the assumption of analyticity. In a system simultaneously coupled to several baths at different temperatures, the nonanalytic potential arises from the different density of states of the baths. In periodically drivendissipative systems, the role of multiple baths is played by a single bath transferring energy at different harmonics of the driving frequency. The meanfield critical exponents become dependent on the lowenergy features of the two most singular baths. We propose an extension beyond mean field.
Stefanos Kourtis, Claudio Chamon, Eduardo R. Mucciolo, Andrei E. Ruckenstein
SciPost Phys. 7, 060 (2019) ·
published 12 November 2019

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We introduce tensor network contraction algorithms for counting satisfying assignments of constraint satisfaction problems (#CSPs). We represent each arbitrary #CSP formula as a tensor network, whose full contraction yields the number of satisfying assignments of that formula, and use graph theoretical methods to determine favorable orders of contraction. We employ our heuristics for the solution of #Phard counting boolean satisfiability (#SAT) problems, namely monotone #1in3SAT and #CubicVertexCover, and find that they outperform stateoftheart solvers by a significant margin.