A unified picture of ferromagnetism, quasi-long range order and criticality in random field models

Abstract

By applying the recently developed nonperturbative functional renormalization group (FRG) approach, we study the interplay between ferromagnetism, quasi-long range order (QLRO) and criticality in the $d$-dimensional random field O(N) model in the whole ($N$, $d$) diagram. Even though the "dimensional reduction" property breaks down below some critical line, the topology of the phase diagram is found similar to that of the pure O(N) model, with however no equivalent of the Kosterlitz-Thouless transition. In addition, we obtain that QLRO, namely a topologically ordered "Bragg glass" phase, is absent in the 3--dimensional random field XY model. The nonperturbative results are supplemented by a perturbative FRG analysis to two loops around $d=4$.

arXiv comment4 pages, 4 figures

References in corpus (16)

• Non-Perturbative Renormalization Flow in Quantum Field Theory and Statistical Physics
• Elastic theory of flux lattices in presence of weak disorder
• Elastic Theory of pinned flux lattices
• Vortex-glass phases in type-II superconductors
• Nonperturbative renormalization group approach to frustrated magnets
• Topological Defects in the Random-Field XY Model and Randomly Pinned Vortex Lattices
• Topological Defects in the Random-Field XY Model and the Pinned Vortex Lattice to Vortex Glass Transition in Type-II Superconductors
• Stability of Elastic Glass Phases in Random Field XY Magnets and Vortex Lattices in Type II Superconductors
• Nonperturbative Renormalization Flow and Essential Scaling for the Kosterlitz-Thouless Transition
• Functional Renormalization Group and the Field Theory of Disordered Elastic Systems
• Topological Order in the Vortex Glass Phase of High-Temperature Superconductors
• Nonperturbative functional renormalization group for random field models: the way out of dimensional reduction
• Quasi-long range order in glass states of impure liquid crystals, magnets, and superconductors
• Quasi-long-range order in the random anisotropy Heisenberg model: functional renormalization group in 4-εdimensions
• Critical Phenomena in Continuous Dimension
• No quasi-long-range order in strongly disordered vortex glasses: a rigorous proof

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