Publication: Microcanonical finite-size scaling in second-order phase transitions with diverging specific heat
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2009-11-06
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American Physical Society
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Abstract
A microcanonical finite-size ansatz in terms of quantities measurable in a finite lattice allows extending phenomenological renormalization the so-called quotients method to the microcanonical ensemble. The ansatz is tested numerically in two models where the canonical specific heat diverges at criticality, thus implying Fisher renormalization of the critical exponents: the three-dimensional ferromagnetic Ising model and the two-dimensional four-state Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows simulating systems as large as L = 1024 Potts or L= 128 (Ising). The quotients method provides accurate determinations of the anomalous dimension, η, and of the (Fisher-renormalized) thermal ν exponent. While in the Ising model the numerical agreement with our theoretical expectations is very good, in the Potts case, we need to carefully incorporate logarithmic corrections to the microcanonical ansatz in order to rationalize our data.
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© 2009 The American Physical Society. We have been partly supported through Research Contracts No. FIS2006-08533-C03, No. FIS2007-60977 MICINN, Spain, and No. GR58/08, 910383 Banco de Santander-UCM. The simulations for this work were performed at BIFI.
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