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Free energy in spin glass models with conventional order
Published 18 Jan 2024 in cond-mat.dis-nn, math-ph, math.MP, and math.PR | (2401.10223v1)
Abstract: Recently, [arXiv:2302.01361] considered spin glass models with additional conventional order parameters characterizing single-replica properties. These parameters are distinct from the standard order parameter used to measure correlations between replicas. A "min-max" formula for the free energy was prescribed in [arXiv:2302.01361]. We rigorously verify this prescription in the setting of vector spin glass models featuring additional deterministic spin interactions. Notably, our results can be viewed as a generalization of the Parisi formula for vector spin glass models in [arXiv:1512.04441], where the order parameter for self-overlap is already present.
- C. L. Baldwin and B. Swingle. Revisiting the replica trick: Competition between spin glass and conventional order. Journal of Statistical Physics, 190(7):125, Jul 2023.
- M. Bardi and L. C. Evans. On hopf’s formulas for solutions of Hamilton–Jacobi equations. Nonlinear Analysis: Theory, Methods & Applications, 8(11):1373–1381, 1984.
- E. Bates and Y. Sohn. Free energy in multi-species mixed p-spin spherical models. Electronic Journal of Probability, 27:1–75, 2022.
- E. Bates and Y. Sohn. Parisi formula for balanced Potts spin glass. arXiv preprint arXiv:2310.06745, 2023.
- Statistical inference of finite-rank tensors. Annales Henri Lebesgue, 5:1161–1189, 2022.
- H.-B. Chen. On the self-overlap in vector spin glasses. arXiv preprint arXiv:2311.09880, 2023.
- H.-B. Chen. Self-overlap correction simplifies the Parisi formula for vector spins. Electronic Journal of Probability, 28(none):1 – 20, 2023.
- On the free energy of vector spin glasses with non-convex interactions. arXiv preprint arXiv:2311.08980, 2023.
- W.-K. Chen. The Aizenman-Sims-Starr scheme and Parisi formula for mixed p-spin spherical models. Electronic Journal of Probability, 18:1–14, 2013.
- T. Dominguez and J.-C. Mourrat. Statistical mechanics of mean-field disordered systems: a Hamilton-Jacobi approach. Preprint, arXiv:2311.08976, 2023.
- F. Guerra. Broken replica symmetry bounds in the mean field spin glass model. Comm. Math. Phys., 233(1):1–12, 2003.
- Matrix analysis. Cambridge university press, 2012.
- Hopf formula and multitime Hamilton–Jacobi equations. Proceedings of the American Mathematical Society, 96(1):79–84, 1986.
- P. Mottishaw. First-order spin glass transitions: an exact solution. Europhysics Letters, 1(8):409, 1986.
- J.-C. Mourrat. Nonconvex interactions in mean-field spin glasses. Probab. Math. Phys., 2(2):281–339, 2021.
- J.-C. Mourrat. The Parisi formula is a Hamilton-Jacobi equation in Wasserstein space. Canad. J. Math., 74(3):607–629, 2022.
- J.-C. Mourrat. Free energy upper bound for mean-field vector spin glasses. Ann. Inst. Henri Poincaré Probab. Stat., 59(3):1143–1182, 2023.
- J.-C. Mourrat and D. Panchenko. Extending the Parisi formula along a Hamilton-Jacobi equation. Electronic Journal of Probability, 25:Paper No. 23, 17, 2020.
- D. Panchenko. Free energy in the generalized Sherrington–Kirkpatrick mean field model. Rev. Math. Phys., 17(7):793–857, 2005.
- D. Panchenko. The Sherrington–Kirkpatrick Model. Springer Monographs in Mathematics. Springer, New York, 2013.
- D. Panchenko. The Parisi formula for mixed p𝑝pitalic_p-spin models. The Annals of Probability, 42(3):946–958, 2014.
- D. Panchenko. The free energy in a multi-species Sherrington–Kirkpatrick model. Ann. Probab., 43(6):3494–3513, 2015.
- D. Panchenko. Free energy in the Potts spin glass. Ann. Probab., 46(2):829–864, 2018.
- D. Panchenko. Free energy in the mixed p𝑝pitalic_p-spin models with vector spins. Ann. Probab., 46(2):865–896, 2018.
- G. Parisi. Infinite number of order parameters for spin-glasses. Phys. Rev. Lett., 43(23):1754, 1979.
- G. Parisi. A sequence of approximated solutions to the SK model for spin glasses. J. Phys. A, 13(4):L115–L121, 1980.
- R. T. Rockafellar. Convex Analysis, volume 36. Princeton university press, 1970.
- D. Ruelle. A mathematical reformulation of Derrida’s REM and GREM. Communications in Mathematical Physics, 108:225–239, 1987.
- M. Talagrand. Free energy of the spherical mean field model. Probab. Theory Related Fields, 134(3):339–382, 2006.
- M. Talagrand. The Parisi formula. Ann. of Math. (2), 163(1):221–263, 2006.
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