Analysis of the low-temperature phase in the two-dimensional long-range diluted XY model

Article

关键词: MERMIN-WAGNER THEOREM;    CRITICAL-BEHAVIOR;    TRANSITIONS;    CROSSOVER;    SYSTEMS;   

DOI  :  10.1103/PhysRevB.100.054203

来源: SCIE

【 摘 要 】

The critical behavior of statistical models with long-range interactions exhibits distinct regimes as a function of rho, the power of the interaction strength decay. For large enough rho, rho >rho(sr), the critical behavior is observed to coincide with that of the short-range model. However, there are controversial aspects regarding this picture, one of which is the value of the short-range threshold rho(sr) in the case of the long-range XY model in two dimensions. We study the 2D XY model on the diluted graph, a sparse graph obtained from the 2D lattice by rewiring links with probability decaying with the Euclidean distance of the lattice as vertical bar r vertical bar(-rho), which is expected to feature the same critical behavior of the long-range model. Through Monte Carlo sampling and finite-size analysis of the spontaneous magnetization and of the Binder cumulant, we present numerical evidence that rho(sr) = 4. According to such a result, one expects the model to belong to the Berezinskii-Kosterlitz-Thouless universality class for rho >= 4, and to present a second-order transition for rho < 4.

【 授权许可】

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