{
  "id": "1801.09779",
  "version": "v1",
  "published": "2018-01-29T22:05:17.000Z",
  "updated": "2018-01-29T22:05:17.000Z",
  "title": "Multicritical point on the de Almeida-Thouless line in spin glasses in $d>6$ dimensions",
  "authors": [
    "M. A. Moore",
    "N. Read"
  ],
  "comment": "5 pages",
  "categories": [
    "cond-mat.stat-mech",
    "cond-mat.dis-nn"
  ],
  "abstract": "The de Almeida-Thouless (AT) line in Ising spin glasses is the phase boundary in the temperature $T$ and magnetic field $h$ plane below which replica symmetry is broken. Using perturbative renormalization group (RG) methods, we show that when the dimension $d$ of space is just above $6$ there is a multicritical point (MCP) on the AT line, which separates a low-field regime, in which the critical exponents have mean-field values, from a high-field regime where the RG flows run away to infinite coupling strength; as $d$ approaches $6$ from above, the location of the MCP approaches the zero-field critical point exponentially in $1/(d-6)$. Thus on the AT line perturbation theory for the critical properties breaks down at sufficiently large magnetic field even above $6$ dimensions, as well as for all non-zero fields when $d\\leq 6$ as was known previously. We calculate the exponents at the MCP to first order in $\\varepsilon=d-6>0$. The fate of the MCP as $d$ increases from just above 6 to infinity is not known.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2018-01-29T22:05:17.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spin glasses",
      "multicritical point",
      "almeida-thouless line",
      "rg flows run away",
      "sufficiently large magnetic field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}