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Order by disorder and phase transitions

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In most phase transitions, the low temperature phase possesses a broken symmetry, that is restored above a critical temperature (with the notable exception of topological phase transitions). This broken symmetry is associated to a non-zero order parameter, and the ground state(s) (at T=0) usually maximizes(s) this order parameter. This is not the case in the presence of order by disorder, where entropic effects are responsible for the enhancement of the order parameter. This situation occurs in the Vesignieite compound BaCu3V2O8(OH)2, a Mott insulator modeled by a J1-J3 Heisenberg model on the kagome lattice (with first and third neighbor interactions). The nature of the classical ground state and the possible phase transitions are investigated through analytical and numerical calculations. This model has many similarities with the J1-J2 square lattice, known to develop a collinear phase for J2>J1|/2 through the order by disorder mechanism. In both model, the limit of large J2 or J3 gives several decoupled sublattices and J1 does not lift the ground state degeneracy. On both lattices, collinear spin configurations are favored by fluctuations, giving rise to a discrete order parameter and to a finite temperature phase transition. On the kagome lattice, a q=4 Potts parameter emerges, against a Z2 on the square lattice. Effect of quantum fluctuations are studied through linear spin wave approximation and high temperature expansions of the S=1/2 model.

Reference: V. Grison et al, Phys.Rev.B 102, 214424 (2020)

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