标题： 平均场自旋玻璃的基态与三自旋耦合 显示英文标题

标题： Ground States of the Mean-Field Spin Glass with 3-Spin Couplings

摘要： 我们使用启发式优化方法进行大规模计算，以低系统误差确定平均场$p$自旋玻璃模型的基态构型，该模型具有$p=3$。在这里，一个$N$伊辛自旋系统中的所有可能三元组都通过键连接。该模型最近引起了兴趣，因为它表现出“重叠间隙条件”，这应该使得在与$p=2$情况（更广为人知的谢林顿-基尔帕特里克模型（SK））相比时，用局部搜索方法渐近地找到基态变得困难。事实上，即使对于我们的启发式方法，找到$p=3$的良好近似也比找到 SK 的更加昂贵。与 SK 相比，$p=3$的基态行为在其他方面也相当不同。对于 SK，对于大系统尺寸$N\to\infty$的系综平均基态能量密度及其分布的宽度，有限尺寸修正以非整数指数异常变化。 在$p=3$的情况下，能量密度及其分布似乎分别与$\ln N/N$和$1/N$的修正成比例。 分布本身与 Gumbel 形式一致。 更为明显的是，在键稀释的情况下， SK 之前已经表明异常修正指数随着键密度有显著变化，而在$p=3$中则没有发现这种变化。 因此，对于三自旋模型，所有测量的修正与随机能量模型（REM）中的修正相同，对应于$p=\infty$。 这表明所有$p$自旋模型，当$p\geq3$时，其基态修正与 REM 中的一致。 显示英文摘要

摘要： We use heuristic optimization methods in extensive computations to determine with low systematic error ground state configurations of the mean-field $p$-spin glass model with $p=3$. Here, all possible triplets in a system of $N$ Ising spins are connected with a bond. This model has been of recent interest, since it exhibits the ``overlap gap condition'', which should make it prohibitive to find ground states asymptotically with local search methods when compared, for instance, with the $p=2$ case better-known as the Sherrington-Kirkpatrick model (SK). Indeed, it proves more costly to find good approximations for $p=3$ than for SK, even for our heuristic. Compared to SK, the ground-state behavior for $p=3$ is quite distinct also in other ways. For SK, finite-size corrections for large system sizes $N\to\infty$ of both, the ensemble average over ground state energy densities and the width of their distribution, vary anomalously with non-integer exponents. In the $p=3$ case here, the energy density and its distribution appear to scale with $\ln N/N$ and $1/N$ corrections, respectively. The distribution itself is consistent with a Gumbel form. Even more stark is the contrast for the bond-diluted case, where SK has shown previously a notable variation of the anomalous corrections exponent with the bond density, while for $p=3$ no such variation is found here. Hence, for the 3-spin model, all measured corrections scale the same as for the random energy model (REM), corresponding to $p=\infty$. This would suggest that all $p$-spin models with $p\geq3$ exhibit the same ground-state corrections as in REM.