非对称复耦合广义Baxter-Wu模型相图的周期性驱动修正
Periodicity-driven revision of the phase diagram of the generalized Baxter-Wu model with asymmetric complex couplings
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中文总结 AI 辅助
本研究修正了非对称复耦合广义Baxter-Wu模型的相图，通过蒙特卡洛模拟明确了其自对偶线的临界阈值条件，澄清了平均符号探测相变的局限性，并评估了Wang-Landau方法的应用局限。
中文摘要 AI 辅助
已知具有非对称复耦合的广义Baxter-Wu（GBW）模型的常规自对偶线为sinh(2K)=±cos(2φ)，其中K和φ分别为耦合的实部与虚部。我们证明这些线并不完整：配分函数的周期性由捆绑玻尔兹曼权重的余弦因子编码，会产生额外的自对偶线sinh(2K)=±sin(2φ)。在完整自对偶候选集的指导下，我们使用蛮力重加权（Metropolis）方法和Wang-Landau方法进行蒙特卡洛模拟。模拟表明，配分函数极小值φ_{Z_min}=(2n+1)π/8处的自对偶线构成一个临界阈值：当|K|≥(1/2)arsinh(cos(π/4))≈0.32924时，它们是真实的临界边界；而当|K|较小时则不是。在φ_{Z_min}处，符号问题最为严重，有限尺寸标度修正也最大；因此，温度扫描中在相边界下方观测到的局部峰值是有限尺寸伪影，而非真实的新相。我们进一步阐明了平均符号及其导数在探测相变方面的能力与局限性，特别是φ_{Z_min}处平均符号的负峰值并不对应真实的相变。我们还评估了Wang-Landau方法，该方法虽形式上规避了符号问题，但仍面临指数壁垒。
英文摘要
The conventional self-dual lines of the generalized Baxter-Wu (GBW) model with asymmetric complex couplings are known to be $\sinh(2K)=\pm \cos(2ϕ)$, where $K$ and $ϕ$ are the real and imaginary parts of the coupling. We demonstrate that these lines are incomplete: the periodicity of the partition function, encoded in the cosine factor of the bundled Boltzmann weight, generates additional self-dual lines $\sinh(2K)=\pm \sin(2ϕ)$. Guided by the complete set of self-dual candidates, we perform Monte Carlo simulations using brute-force reweighting (Metropolis) and the Wang-Landau methods. Simulations indicate that the self-dual lines at the partition-function minima $ϕ_{\mathcal{Z}_{\min}}=(2n+1)π/8$ constitute a critical threshold. They are genuine critical boundaries for $|K| \ge \frac{1}{2}\operatorname{arsinh}(\cos(π/4)) \approx 0.32924$, while for smaller $|K|$ they are not. At $ϕ_{\mathcal{Z}_{\min}}$, the sign problem is most severe and finite-size scaling corrections are largest; the local peak observed below the phase boundary in the temperature scan is thus a finite-size artifact, not a genuine new phase. We further clarify the capability and limitations of the average sign and its derivatives for detecting phase transitions. In particular, the negative peak of the average sign at $ϕ_{\mathcal{Z}_{\min}}$ does not correspond to a genuine phase transition. We also evaluate the Wang-Landau method, which, despite formally circumventing the sign problem, still faces the exponential barrier.
