New phenomena in the random field Ising model

Abstract

We reconsider Ising spins in a Gaussian random field within the replica formalism. The corresponding continuum model involves several coupling constants beyond the single one which was considered in the standard ${\varphi }^4$ theory approach. These terms involve more than one replica, and therefore in a mean field theory they do not contribute to the zero-replica limit. However the fluctuations involving those extra terms are singular on the Curie line below eight dimensions, and by the time one reaches the dimension six, it is necessary to keep them in the renormalization group analysis. As a result it is found that there is no stable fixed point of order $(6-d)$. Whether this means that there is no expansion in powers of $(6-d)$, or that the transition is driven to first order by these fluctuations, is difficult to decide at this level, but it explains the failure of the $(d,d-2)$ correspondence. In this work we have not considered the possibility of a glassy phase in the would-be paramagnetic region, but in a subsequent work we shall present evidence for replica symmetry breaking in dimension lower than six.

9 pages, latex, no figure

Cited by in corpus (35)

• Disorder-Induced Critical Phenomena in Hysteresis: Numerical Scaling in Three and Higher Dimensions
• Functional Renormalization Group and the Field Theory of Disordered Elastic Systems
• Non-Perturbative Functional Renormalization Group for Random Field Models and Related Disordered Systems. I: Effective Average Action Formalism
• Scale Invariance in disordered systems: the example of the Random Field Ising Model
• Elusive Glassy Phase in the Random Field Ising Model
• New algorithm and results for the three-dimensional random field Ising Model
• Logarithmic conformal field theories as limits of ordinary CFTs and some physical applications
• Evidence for Supersymmetry in the Random-Field Ising Model at D = 5
• Stability of Random-Field and Random-Anisotropy Fixed Points at large N
• Random field spin models beyond one loop: a mechanism for decreasing the lower critical dimension
• Restoration of dimensional reduction in the random-field Ising model at five dimensions
• Functional renormalization group at large N for random manifolds
• First-order transition features of the 3D bimodal random-field Ising model
• Ground state numerical study of the three-dimensional random field Ising model
• Review of recent developments in the random-field Ising model
• The fate of Parisi-Sourlas supersymmetry in Random Field models
• The renormalization group flow in field theories with quenched disorder
• Random Field Ising Model and Parisi-Sourlas Supersymmetry. Part II. Renormalization Group
• No spin glass phase in ferromagnetic random-field random-temperature scalar Ginzburg-Landau model
• Derivation of the Functional Renormalization Group Beta-Function at order 1/N for Manifolds Pinned by Disorder
• Critical behaviour in two-dimensional Coulomb Glass at zero temperature
• Renormalization group for measurement and entanglement phase transitions
• On the nature of the phase transition in the three-dimensional random field Ising model
• Temporally disordered Ising models
• Dimensional Reduction by Conformal Bootstrap
• Replica-symmetric solutions of a dilute Ising ferromagnet in a random field
• On the phase transition of the 3D random field Ising model
• Random-field p-spin glass model on regular random graphs
• Disordered $\lambda {\phi }^4+\rho {\phi }^6$ Landau-Ginzburg model
• Dimensional Reduction for Directed Branched Polymers
• Hierarchical Reference Theory of critical fluids in disordered porous media
• Nature and number of distinct phases in the random field Ising model
• Renormalization group for the probability distribution of magnetic impurities in a random-field ${\varphi }^4$ model
• Finite-Size Effects in Disordered $\lambda {\varphi }^4$ Model
• First Order Transition in Two Dimensional Coulomb Glass