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Binder ratio in the two-dimensional q-state clock model
Luong Minh Tuan1,2, Ta Thanh Long1, Duong Xuan Nui1,3
1Advanced Institute for Science and Technology, Hanoi University of Science and Technology, Hanoi 10000, Vietnam.
Abstract:
We study phase transition properties of the two-dimensional q-state clock model by an extensive Monte Carlo simulation. By analyzing the Binder ratio and its temperature derivative, we confirm that the two-dimensional q-state clock model exhibits two distinct Kosterlitz-Thouless phase transitions for q=5,6 but it has one second-order phase transition for q=4. The critical temperatures are estimated quite accurately from the crossing behavior of the Binder ratio (for q<5) and from negative divergent dips of the derivative of the Binder ratio (for q≥5) around these critical points. We also calculate the correlation length, the helicity modulus, and the derivative of the helicity modulus, and analyze their behaviors in different phases in detail.
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