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Methods of Ex Situ and In Situ Investigations of Structural Transformations: The Case of Crystallization of Metallic Glasses
Published on: June 7, 2018
Unified picture of ferromagnetism, quasi-long-range order, and criticality in random-field models
Matthieu Tissier1, Gilles Tarjus
1LPTMC, Université Pierre et Marie Curie, boîte 121, 4 Place Jussieu, 75252 Paris cédex 05, France.
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.
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