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arXiv:1612.08568 · The European Physical Journal B

Dynamic canonical and microcanonical transition matrix analyses of critical behavior

David O. Yevick, Yong Hwan Lee

Published Apr 28, 2017• 7 citations
arXivHTMLPDF
DOI
10.1140/epjb/e2017-70747-x

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Abstract This article investigates the pseudo phase transition behavior of the six-state clock model on two-dimensional finite-size lattices. By employing the Wang–Landau sampling method and microcanonical inflection-point analysis, we identified two phase transition points and classified both as continuous transitions within the microcanonical framework. Using Metropolis sampling and canonical ensemble analysis, we verified the accuracy of the transition points obtained from the microcanonical approach and further pinpointed the location of a fourth-order dependent transition with high accuracy. Moreover, the fourth-order dependent transition points extracted from two canonical order parameters—the average cluster perimeter and the M Z 6 symmetry—are in excellent agreement and consistently reinforce each other. Through a detailed analysis of the M Z 6 symmetry, we further demonstrate that the position of this fourth-order dependent transition may function as a critical transition warning indicator for both primary phase transitions in the system.