Critical droplets and replica symmetry breaking
We show that the notion of critical droplets is central to an understanding of the nature of ground states in the Edwards–Anderson–Ising model of a spin glass in arbitrary dimensions. Given a specific ground state, we suppose that the coupling value for a given edge is varied with all other coupling...
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Frontiers Media S.A.
2024-11-01
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| Series: | Frontiers in Physics |
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| Online Access: | https://www.frontiersin.org/articles/10.3389/fphy.2024.1473378/full |
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| author | C. M. Newman C. M. Newman D. L. Stein D. L. Stein D. L. Stein |
| author_facet | C. M. Newman C. M. Newman D. L. Stein D. L. Stein D. L. Stein |
| author_sort | C. M. Newman |
| collection | DOAJ |
| description | We show that the notion of critical droplets is central to an understanding of the nature of ground states in the Edwards–Anderson–Ising model of a spin glass in arbitrary dimensions. Given a specific ground state, we suppose that the coupling value for a given edge is varied with all other couplings held fixed. Beyond some specific value of the coupling, a droplet will flip, leading to a new ground state; we refer to this as the critical droplet for that edge and ground state. We show that the distribution of sizes and energies over all edges for a specific ground state can be used to determine which of the leading scenarios for the spin glass phase is correct. In particular, the existence of low-energy interfaces between incongruent ground states, as predicted by replica symmetry breaking, is equivalent to the presence of critical droplets, whose boundaries comprise a positive fraction of edges in the infinite lattice. |
| format | Article |
| id | doaj-art-fd623d1edaf24fa580ad2d7569cf5e29 |
| institution | Kabale University |
| issn | 2296-424X |
| language | English |
| publishDate | 2024-11-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Physics |
| spelling | doaj-art-fd623d1edaf24fa580ad2d7569cf5e292024-11-14T08:19:43ZengFrontiers Media S.A.Frontiers in Physics2296-424X2024-11-011210.3389/fphy.2024.14733781473378Critical droplets and replica symmetry breakingC. M. Newman0C. M. Newman1D. L. Stein2D. L. Stein3D. L. Stein4Courant Institute of Mathematical Sciences, New York University, New York, NY, United StatesNYU-ECNU Institute of Mathematical Sciences at NYU Shanghai, Shanghai, ChinaDepartment of Physics and Courant Institute of Mathematical Sciences, New York University, New York, NY, United StatesNYU-ECNU Institutes of Physics and Mathematical Sciences at NYU Shanghai, Shanghai, ChinaSanta Fe Institute, Santa Fe, NM, United StatesWe show that the notion of critical droplets is central to an understanding of the nature of ground states in the Edwards–Anderson–Ising model of a spin glass in arbitrary dimensions. Given a specific ground state, we suppose that the coupling value for a given edge is varied with all other couplings held fixed. Beyond some specific value of the coupling, a droplet will flip, leading to a new ground state; we refer to this as the critical droplet for that edge and ground state. We show that the distribution of sizes and energies over all edges for a specific ground state can be used to determine which of the leading scenarios for the spin glass phase is correct. In particular, the existence of low-energy interfaces between incongruent ground states, as predicted by replica symmetry breaking, is equivalent to the presence of critical droplets, whose boundaries comprise a positive fraction of edges in the infinite lattice.https://www.frontiersin.org/articles/10.3389/fphy.2024.1473378/fullspin glassesground statescritical dropletsreplica symmetry breakingground-state interfaces |
| spellingShingle | C. M. Newman C. M. Newman D. L. Stein D. L. Stein D. L. Stein Critical droplets and replica symmetry breaking Frontiers in Physics spin glasses ground states critical droplets replica symmetry breaking ground-state interfaces |
| title | Critical droplets and replica symmetry breaking |
| title_full | Critical droplets and replica symmetry breaking |
| title_fullStr | Critical droplets and replica symmetry breaking |
| title_full_unstemmed | Critical droplets and replica symmetry breaking |
| title_short | Critical droplets and replica symmetry breaking |
| title_sort | critical droplets and replica symmetry breaking |
| topic | spin glasses ground states critical droplets replica symmetry breaking ground-state interfaces |
| url | https://www.frontiersin.org/articles/10.3389/fphy.2024.1473378/full |
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