Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions

Campostrini, Massimo; Nespolo, Jacopo; Pelissetto, Andrea; Vicari, Ettore

doi:10.1103/physreve.91.022108

Cited by 12 publications

(18 citation statements)

References 102 publications

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“…We finally mention that an interesting extension of this study concerns the effects of inhomogeneous conditions at FOQTs, such as those induced by space dependent external fields. Nontrivial scaling phenomena emerge also in this case, with respect to the length scale of the induced inhomogeneity, in the space transition region between the two phases [46]. The non degenerate, even, ground state level E0 approaches the (q −1) times degenerate multiplet of energy E1 in the ordered phase g < 1.…”

Section: Discussionmentioning

confidence: 81%

Finite-size scaling at the first-order quantum transitions of quantum Potts chains

et al. 2015

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We investigate finite-size effects in quantum systems at first-order quantum transitions. For this purpose we consider the one-dimensional q-state Potts models which undergo a first-order quantum transition for any q > 4, separating the quantum disordered and ordered phases with a discontinuity in the energy density of the ground state. The low-energy properties around the transition show finite-size scaling, described by general scaling ansatzes with respect to appropriate scaling variables. The size dependence of the scaling variables presents a particular sensitiveness to boundary conditions, which may be considered as a peculiar feature of first-order quantum transitions.

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Section: Discussionmentioning

confidence: 81%

Finite-size scaling at the first-order quantum transitions of quantum Potts chains

et al. 2015

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“…Finally, we mention that the mixed Potts model resembles a square-lattice quantum Potts antiferromagnet in a transverse field [27][28][29]. The z dimension in the classical model corresponds with imaginary time in the Suzuki-Trotter formulation of the quantum model.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Emergent O(n) symmetry in a series of three-dimensional Potts models

2016

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We study the q-state Potts model on a simple cubic lattice with ferromagnetic interactions in one lattice direction, and antiferromagnetic interactions in the other two directions. As the temperature T decreases, the system undergoes a second-order phase transition that fits in the universality class of the three-dimensional O(n) model with n = q − 1. This conclusion is based on the estimated critical exponents, and histograms of the order parameter. At even smaller T we find, for q = 4 and 5, a first-order transition to a phase with a different type of long-range order. This long-range order dissolves at T = 0, and the system effectively reduces to a disordered two-dimensional Potts antiferromagnet. These results are obtained by means of Monte Carlo simulations and finite-size scaling.

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“…In the case of FOTs the effective length-scale exponent ν controlling the FSS at T c generally depends on the geometry of the lattice [38][39][40][41], i.e., whether it is square L 2 or slab-like L ⊥ × L with L ≫ L ⊥ , and on the boundary conditions [40][41][42].…”

Section: The Length-scale Exponent νmentioning

confidence: 99%

Off-equilibrium scaling behaviors across first-order transitions

Panagopoulos¹,

Vicari²

2015

Phys. Rev. E

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We study off-equilibrium behaviors at first-order transitions (FOTs) driven by a time dependence of the temperature across the transition point T(c), such as the linear behavior T(t)/T(c)=1±t/t(s) where t(s) is a time scale. In particular, we investigate the possibility of nontrivial off-equilibrium scaling behaviors in the regime of slow changes, corresponding to large t(s). We consider the two-dimensional Potts models, which provide an ideal theoretical laboratory to investigate issues related to FOTs driven by thermal fluctuations. We put forward general ansatzes for off-equilibrium scaling behaviors around the time t=0 corresponding to T(c). Then we present numerical results for the q=10 and 20 Potts models. We show that off-equilibrium scaling behaviors emerge at FOTs with relaxational dynamics, when appropriate boundary conditions are considered, such as mixed boundary conditions favoring different phases at the opposite sides of the system, which enforce an interface in the system.

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Scaling phenomena driven by inhomogeneous conditions at first-order quantum transitions

Cited by 12 publications

References 102 publications

Finite-size scaling at the first-order quantum transitions of quantum Potts chains

Finite-size scaling at the first-order quantum transitions of quantum Potts chains

Emergent O(n) symmetry in a series of three-dimensional Potts models

Off-equilibrium scaling behaviors across first-order transitions

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