Microcanonical finite-size scaling in specific heat diverging 2nd order phase transitions

Abstract

A Microcanonical Finite Site Ansatz in terms of quantities measurable in a Finite Lattice allows to extend 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 3D ferromagnetic Ising model and the 2D four-states Potts model (where large logarithmic corrections are known to occur in the canonical ensemble). A recently proposed microcanonical cluster method allows to simulate systems as large as L=1024 (Potts) or L=128 (Ising). The quotients method provides extremely accurate determinations of the anomalous dimension and of the (Fisher-renormalized) thermal $\nu$ exponent. While in the Ising model the numerical agreement with our theoretical expectations is impressive, in the Potts case we need to carefully incorporate logarithmic corrections to the microcanonical Ansatz in order to rationalize our data.

13 pages, 8 figures

References in corpus (7)

• 25th-order high-temperature expansion results for three-dimensional Ising-like systems on the simple cubic lattice
• Scaling Relations for Logarithmic Corrections
• Self-Consistent Scaling Theory for Logarithmic Correction Exponents
• Microcanonical Approach to the Simulation of First-Order Phase Transitions
• Continuous phase transitions with a convex dip in the microcanonical entropy
• First order transition in a three dimensional disordered system
• Fisher Renormalization for Logarithmic Corrections

Cited by in corpus (4)

• Numerical test of the Cardy-Jacobsen conjecture in the site-diluted Potts model in three dimensions
• Two-dimensional dilute Baxter-Wu model: Transition order and universality
• Equivalence between microcanonical methods for lattice models
• A Microcanonical Inflection Point Analysis via Parametric Curves and its Relation to the Zeros of the Partition Function