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arXiv · 2108.11566

Non-monotonic behavior of the Binder Parameter in the discrete spin systems

Hiroshi Watanabe·Yuichi Motoyama·Satoshi Morita·Naoki Kawashima
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Abstract

We study a non-monotonic behavior of the Binder parameter, which appears in the discrete spin systems. We show that the Binder parameters of the Potts model are non-monotonic for $q=3$ and $4$, while they are monotonic for the Ising case ($q=2$). Using the Fortuin-Kasteleyn graph representation, we find that the improved estimator of the Binder parameter consists of two terms with values only in high- and low-temperature regions. The non-monotonic behavior is found to originate from the low-temperature term. With the appropriately defined order parameter, we can reduce the influence of the low-temperature term, and as a result, the non-monotonic behavior can also be reduced. We propose new definitions of the order parameter, which reduces or eliminates the non-monotonic behavior of the Binder parameter in a system for which the improved estimator of the Binder parameter is unknown.

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Hiroshi Watanabe, Yuichi Motoyama, Satoshi Morita, Naoki Kawashima. 2021-08-26. Non-monotonic behavior of the Binder Parameter in the discrete spin systems. https://doi.org/10.1093/ptep/ptad022

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