We investigate the phase diagram and critical properties of the two-dimensional classical XY model with interactions decaying as $1/r^{2+\sigma}$. At the marginal case $\sigma=2$, we show that the low-temperature phase is characterized by logarithmic quasi-long-range order (log-QLRO), where spin correlations decay as a...
The crossover from long-range (LR) to short-range (SR) criticality in percolation has remained unsettled because previous renormalization-group (RG) analysis within the $\epsilon'=3\sigma-d$ expansion fixes the anomalous dimension at $\eta=2-\sigma$, whereas SR percolation has $\eta_{\rm SR}<0$ near $d=6$. Sak's matchi...
Zhiyi Li, Kun Chen, Zhi-Jie Fan et al.· 0 citations
We study the one-dimensional long-range self-avoiding walk in the grand-canonical ensemble where the statistical weight of a jump of length $r$ decays algebraically as $r^{-(d+\sigma)}$. Using large-scale Monte Carlo simulations with an efficient irreversible update scheme, we obtain high-precision estimates of the cri...
Jiang Zhou, Zi-Yu Liu, Peng-Cheng Hou et al.· 0 citations
We present a comprehensive Monte Carlo study of two-dimensional bond percolation with algebraically decaying connection probabilities $p(r)\propto 1/r^{2+\sigma}$, establishing the universality diagram in the long-range (LR) regime for $\sigma\le2$. Using the event-based ensemble method, we simulate systems with linear...
Zi-Yu Liu, Tianning Xiao, Zhi-Jie Fan et al.· 2 citations
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