AI 中文总结
研究通过不可逆变换相关的两个哈密顿量的有限温度相图是否相同，以簇模型插值及其肯尼迪 - 田崎对偶为例，用一维、三维情况及量子蒙特卡罗结果表明不同维度下相图在特定区间存在差异与一致性。
AI 中文摘要
通过不可逆变换相关的两个哈密顿量一定共享相同的有限温度相图吗？对于一个簇模型插值\(H(s)\)及其肯尼迪 - 田崎对偶\(\tilde H(s)\)，该映射是部分等距变换，仅使它们的全加扇区配分函数相等。在一维中，两侧都禁止热序，仅在\(s = \frac{1}{2}\)处有共同的零温度转变。然而在三维中，在\(s = 0\)时不等价就已存在：簇模型有解析的顺磁自由能，而其对偶\(\mathbb{Z}_2\)规范理论在\(T_c \approx 1.31\)处有去禁闭转变。量子蒙特卡罗表明这种不匹配占据插值的有限窗口，在簇模型一侧由自对偶冻结楔标记，在规范理论一侧由去禁闭穹顶标记；一旦两者关闭，两个相图再次一致，在直至共享平凡端点\(s = 1\)的整个剩余区间重合。
英文摘要
Do two Hamiltonians related by a non-invertible transformation necessarily share the same finite-temperature phase diagram? For a cluster-model interpolation $H(s)$ and its Kennedy--Tasaki dual $\tilde H(s)$, the map is a partial isometry and equates only their all-plus-sector partition functions. In one dimension, thermal order is forbidden on both sides, leaving only the common zero-temperature transition at $s=\tfrac12$. In three dimensions, however, the inequivalence is exact already at $s=0$: the cluster model has an analytic paramagnetic free energy, whereas its dual $\mathbb Z_2$ gauge theory has a deconfinement transition at $T_c\approx1.31$. Quantum Monte Carlo shows that the mismatch occupies a finite window of the interpolation, marked by a self-dual frozen wedge on the cluster side and a deconfined dome on the gauge side; once both close the two phase diagrams agree again, coinciding over the entire remaining interval up to the shared trivial endpoint $s=1$.
Comments7+15 pages, 3+4 figures; v2: reference to our companion paper added
