arXiv subjects

Dingyun Yao

Publications and source records attributed to Dingyun Yao.

4 recordsLinked to original sources

arXiv2026

Spontaneous Symmetry Breaking in Two-dimensional Long-range Heisenberg Model

Algebraically decaying interactions $\sim 1/r^{d+σ}$ can lead to nontrivial universality beyond short-range (SR) theories and spontaneous symmetry breaking in low-dimensional systems. We perform large-scale Monte Carlo simulations for the classical long-range (LR) Heisenberg model in two dimensions (2D) up to linear size $L=8192$. We show that the system enters a long-range-ordered phase through a single continuous phase transition for all $σ\leq 2$, including the marginal case $σ=2$. In contrast, for $σ> 2$ it recovers the SR asymptotically free behavior with no finite-temperature transition. This places the LR--SR crossover threshold at $σ_* = 2$. To characterize the ordered phase, we introduce an LR simple random walk with a fixed total length $\mathcal{L} \sim\mathcal{O}(L^d)$. This fixed-$\mathcal L$ walk reproduces the finite-size scaling of the Goldstone-mode fluctuations in the LR Heisenberg model in both two and three dimensions, including the logarithmic scaling at $σ= 2$. These results further motivate a general criterion for the existence of finite-temperature long-range order in LR systems with continuous symmetry in any spatial dimension.

cond-mat.stat-mech↗

arXiv2025

The Nonclassical Regime of the Two-dimensional Long-range XY Model: a Comprehensive Monte Carlo Study

The two-dimensional (2D) XY model plays a crucial role in statistical and condensed matter physics. With the introduction of long-range interactions, the system exhibits a richer set of physical phenomena and a crossover between non-classical and short-range universality classes.In this work, we investigate the 2D XY model with algebraically decaying interactions $\sim 1/r^{2+σ}$, and provide a comprehensive numerical analysis of its thermodynamic properties. We demonstrate that for $σ\leq 2$, the system undergoes a second-order phase transition into a ferromagnetic phase characterized by the emergence of long-range order. In the low-temperature phase, due to the presence of the Goldstone mode, the correlation function saturates to a non-zero constant in the form of a power law for $σ< 2$, with decaying exponent $2-σ$, and in the form of the inverse logarithm of distance for $σ=2$. Moreover, the critical points and exponents are also determined for various $σ$. We provide compelling evidence that the crossover between non-classical and short-range regimes occurs at $σ=2$. This work presents a detailed account of the simulation methodology, extensive numerical data, and new insights into the physics of long-range interacting systems.

cond-mat.stat-mech↗

arXiv2025

Asymptotic Freedom and Finite-size Scaling of Two-dimensional Classical Heisenberg Model

The classical Heisenberg model is one of the most fundamental models in statistical and condensed matter physics. Extensive theoretical and numerical studies suggest that, in two dimensions, this model does not exhibit a finite-temperature phase transition but instead manifests asymptotic freedom. However, some research has also proposed the possibility of a Berezinskii-Kosterlitz-Thouless (BKT) phase transition over the years. In this study, we revisit the classical two-dimensional (2D) Heisenberg model through large-scale simulations with linear system sizes up to $L=16384$. Our Monte-Carlo data, without any extrapolation, clearly reveal an exponential divergence of the correlation length $ξ$ as a function of inverse temperature $β$, a hallmark of asymptotic freedom. Moreover, extrapolating $ξ$ to the thermodynamic limit in the low-temperature regime achieves close agreement with the three-loop perturbative calculations. We further propose a finite-size scaling (FSS) ansatz for $ξ$, demonstrating that the pseudo-critical point $β_L$ diverges logarithmically with $L$. The thermodynamic and finite-size scaling behaviors of the magnetic susceptibility $χ$ are also investigated and corroborate the prediction of asymptotic freedom. Our work provides solid evidence for asymptotic freedom in the 2D Heisenberg model and advances understanding of finite-size scaling in such systems.

cond-mat.stat-mech↗

arXiv2024

Two-dimensional XY Ferromagnet Induced by Long-range Interaction

The crossover between short-range and long-range (LR) universal behaviors remains a central theme in the physics of long-range interacting systems. The competition between LR coupling and the Berezinskii-Kosterlitz-Thouless mechanism makes the problem more subtle and less understood in the two-dimensional (2D) XY model, a cornerstone for investigating low-dimensional phenomena and their implications in quantum computation. We study the 2D XY model with algebraically decaying interaction $\sim1/r^{2+σ}$. Utilizing an advanced update strategy, we conduct large-scale Monte Carlo simulations of the model up to a linear size of $L=8192$. Our results demonstrate continuous phase transitions into a ferromagnetic phase for $σ\leq 2$, which exhibits the simultaneous emergence of a long-ranged order and a power-law decaying correlation function due to the Goldstone mode. Furthermore, we find logarithmic scaling behaviors in the low-temperature phase at $σ= 2$. The observed scaling behaviors in the low-temperature phase for $σ\le 2$ agree with our theoretical analysis. Our findings request further theoretical understandings and can be of practical application in cutting-edge experiments like Rydberg atom arrays.

cond-mat.stat-mech↗