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Abstract: We face the problem of detecting and featuring footprints of quantumcriticality in the finite-temperature behavior of quantum many-body systems.Our strategy is that of comparing the phase diagram of a system displaying aT=0 quantum phase transition with that of its classical limit, in order tosingle out the genuinely quantum effects. To this aim, we consider theone-dimensional Ising model in a transverse field: while the quantum S=1-2Ising chain is exactly solvable and extensively studied, results for theclassical limit infinite S of such model are lacking, and we supply themhere. They are obtained numerically, via the Transfer-matrix method, and theirasymptotic low-temperature behavior is also derived analytically byself-consistent spin-wave theory. We draw the classical phase-diagram accordingto the same procedure followed in the quantum analysis, and the two phasediagrams are found unexpectedly similar: Three regimes are detected also in theclassical case, each characterized by a functional dependence of thecorrelation length on temperature and field analogous to that of the quantummodel. What discriminates the classical from the quantum case are the differentvalues of the exponents entering such dependencies, a consequence of thedifferent nature of zero-temperature quantum fluctuations with respect tothermal ones.



Autor: Alessandro Cuccoli, Alessio Taiti, Ruggero Vaia, Paola Verrucchi

Fuente: https://arxiv.org/







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