TY - JOUR

T1 - Multicritical Point on the de Almeida-Thouless Line in Spin Glasses in d>6 Dimensions

AU - Moore, M. A.

AU - Read, N.

PY - 2018

Y1 - 2018

N2 - 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 six, 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 six from above, 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 a sufficiently large magnetic field even above 6 dimensions, as well as for all nonzero fields when d≤6, as was known previously. We calculate the exponents at the MCP to first order in μ=d-6>0. The fate of the MCP as d increases from just above six to infinity is not known.

AB - 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 six, 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 six from above, 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 a sufficiently large magnetic field even above 6 dimensions, as well as for all nonzero fields when d≤6, as was known previously. We calculate the exponents at the MCP to first order in μ=d-6>0. The fate of the MCP as d increases from just above six to infinity is not known.

UR - http://www.scopus.com/inward/record.url?scp=85044738544&partnerID=8YFLogxK

U2 - 10.1103/PhysRevLett.120.130602

DO - 10.1103/PhysRevLett.120.130602

M3 - Article

AN - SCOPUS:85044738544

SN - 0031-9007

VL - 120

JO - Physical Review Letters

JF - Physical Review Letters

IS - 13

M1 - 130602

ER -