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

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

2005-11-04

arxiv.org/abs/cond-mat/0511096v1

Physics

Condensed Matter

Other Condensed Matter

4 pages, 4 figures

Scientific paper

10.1103/PhysRevLett.96.087202

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 $d=4$.

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