Complexity of the p-spin Hamiltonian with a Non-Rotationally Invariant Potential
Abstract
We investigate the complexity of the Hamiltonian in the pure $p$-spin spin glass model accompanied with a polynomial-type potential on $\mathbb{R}^N$. In this Hamiltonian, the Gaussian field is anisotropic, and the potential lacks rotational invariance. Our main result derives the logarithmic limit for the expected number of critical points in terms of a variational formula. As a consequence, by identifying the critical location of the phase transition from our representation, we provide an upper bound for the ground state energy of the model.
Fields of Study & Subjects
Theoretical and Computational Physics
Random Matrices and Applications
Stochastic processes and statistical mechanics
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 11 February 2026
- Language
- EN
- Document type
- Preprint