Convergence of the Free Energy for Spherical Spin Glasses
نویسندگان
چکیده
We prove that the free energy of any spherical mixed $p$-spin model converges as dimension $N$ tends to infinity. While convergence is a consequence Parisi formula, proof we give independent formula and uses well-known Guerra-Toninelli interpolation method. The latter was invented for models with Ising spins super-additive therefore (normalized by $N$) converges. In case, however, configuration space not product cannot be applied directly. first relate on sphere $N+M$ defined spheres in dimensions $M$ which then apply This yields an approximate super-additivity sufficient convergence.
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ژورنال
عنوان ژورنال: Journal of Statistical Physics
سال: 2022
ISSN: ['0022-4715', '1572-9613']
DOI: https://doi.org/10.1007/s10955-022-02988-2