We evaluate the high temperature limit of the free energy of spin glasses on the hypercube with Hamiltonian $H_N(σ) = σ^T J σ$, where the coupling matrix $J$ is drawn from certain symmetric orthogonally invariant ensembles. Our derivation relates the annealed free energy of these models to a spherical integral, and expresses the limit of the free energy in terms of the limiting spectral measure of the coupling matrix $J$. As an application, we derive the limiting free energy of the Random Orthogonal Model (ROM) at high temperatures, which confirms non-rigorous calculations of Marinari et al. (1994). Our methods also apply to other well-known models of disordered systems, including the SK and Gaussian Hopfield models.
Geometry and temperature chaos in mixed spherical spin glasses at low temperature - the perturbative regime
我们研究了混合球形$p$自旋玻璃模型在低温下的吉布斯测度，在（部分）1-RSB制度，特别是包括，在适当的意义上，接近纯的模型。我们表明，吉布斯措施集中在深临界点周围的（扩展）哈密顿限制到半径$\sqrt N q_\star$，其中$q_\star^2$是最右边的点，在重叠分布的支持球带。我们还表明，相关的临界点是两两正交的两个不同的低温。这使我们能够解释为什么这些模型会出现温度混沌，而不是纯球形模型。
One-sided large deviations for the ground-state energy of spin glasses
NYU-ECNU Institute of Mathematical Sciences, NYU Shanghai（纽约大学-华东师范大学数学科学研究所，上海纽约大学）；Department of Mathematics, ENS Lyon and CNRS（里昂高等师范学校数学系与法国国家科学研究中心）；Department of Mathematics, Syracuse University（雪城大学数学系）；Department of Mathematics, King’s College（国王学院数学系）
Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles
这是“Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles：Announcement of Results”的完整版本，出现在此服务器上，也发表在IMRN 2003，第15号，第15页。821-858.
Uniform Asymptotics for Polynomials Orthogonal With Respect to a General Class of Discrete Weights and Universality Results for Associated Ensembles: Announcement of Results
