Sherrington–Kirkpatrick模型中临界淬火自相关的普适性
Universality of critical quench autocorrelations in the Sherrington–Kirkpatrick model
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具体内容
该稿件研究零场Sherrington–Kirkpatrick热浴动力学在逆温度β=1时的自相关极限。摘要表示，作者证明平稳与淬火自相关的联合泛函收敛，高斯与Rademacher耦合给出相同随机极限。每个格点有速率一的时钟，平均自旋自相关乘以n^{1/3}，等待时间与滞后以n^{2/3}为单位；淬火从独立公平自旋出发，在正等待时间与滞后的紧集上一致收敛，淬火极限随等待时间趋于无穷松弛到平稳极限。手稿为AI产生，未经独立审查或同行评议。
- 作者声称在β=1时证明平稳与淬火自相关的联合泛函收敛，高斯与Rademacher耦合极限相同。
- 平均自旋自相关乘以n^{1/3}，等待时间与滞后以n^{2/3}为单位。
- 淬火从独立公平自旋出发，极限随等待时间趋于无穷松弛到平稳极限。
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英文原始摘要
We prove joint functional convergence of the stationary and quench autocorrelations of zero-field Sherrington–Kirkpatrick heat-bath dynamics at inverse temperature β = 1, with the same random limit for Gaussian and Rademacher couplings. Each site has a rate-one clock, mean spin autocorrelations are multiplied by n1/3, and waiting times and lags are measured in units n2/3. The quench starts from independent fair spins, and convergence is uniform on compact sets of positive waiting times and lags. The quench limit is selected by these initial states and relaxes to the stationary limiting autocorrelation as the waiting time tends to infinity.
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