Metric features of a dipolar model

Casartelli, Mario; Dall’Asta, Luca; Rastelli, E.; Regina, S.

doi:10.1088/0305-4470/37/49/001

Cited by 9 publications

(13 citation statements)

References 18 publications

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“…[13,14,15,16]. For applications in the spirit of our demands, see also [11,12,17,18]. Here we only recall the definitions of Shannon entropy and Rohlin distance.…”

Section: Discussionmentioning

confidence: 99%

Configurations and observables in an Ising model with heat flow

2007

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We study a two dimensional Ising model between thermostats at different temperatures. By applying the recently introduced KQ dynamics, we show that the system reaches a steady state with coexisting phases transversal to the heat flow. The relevance of such complex states on thermodynamic or geometrical observables is investigated. In particular, we study energy, magnetization and metric properties of interfaces and clusters which, in principle, are sensitive to local features of configurations. With respect to equilibrium states, the presence of the heat flow amplifies the fluctuations of both thermodynamic and geometrical observables in a domain around the critical energy. The dependence of this phenomenon on various parameters (size, thermal gradient, interaction) is discussed also with reference to other possible diffusive models.

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“…[13,14,15,16]. For applications in the spirit of our demands, see also [11,12,17,18]. Here we only recall the definitions of Shannon entropy and Rohlin distance.…”

Section: Discussionmentioning

confidence: 99%

Configurations and observables in an Ising model with heat flow

2007

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“…Analytical and Monte Carlo (MC) calculations have shown the following picture: For a fixed coupling δ > 0.4403, the phase diagram initially exhibits the alternating striped spin configurations as described above, characterizing the so called smectic striped phase. As the temperature increases, the initial picture describes a transition into the tetragonal phase [10,11,12,13] characterized by states with orientationally disordered stripes but still preserving some of this structural form, which tends to the completely disordered paramagnetic state. Recent numerical results related to this striped-tetragonal phase transition indicate a continuous transition for h = 1 [14], a clear first-order transition for h = 2 [11,14], a likely weaker first-order transition for h = 3 [14], and a continuous transition for h = 4 [14] and h = 8 [12].…”

Section: Introductionmentioning

confidence: 99%

Phase transitions and autocorrelation times in two-dimensional Ising model with dipole interactions

Rizzi

Alves

2010

Physica B: Condensed Matter

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The two-dimensional Ising model with nearest-neighbor ferromagnetic and long-range dipolar interactions exhibits a rich phase diagram. The presence of the dipolar interaction changes the ferromagnetic ground state expected for the pure Ising model to a series of striped phases as a function of the interaction strengths. Monte Carlo simulations and histogram reweighting techniques applied to multiple histograms are performed to identify the critical temperatures for the phase transitions taking place for stripes of width h = 2 on square lattices. In particular, we aim to study the intermediate nematic phase, which is observed for large lattice sizes only. For these lattice sizes, we calculate the critical temperatures for the striped-nematic and nematic-tetragonal transitions, critical exponents, and the bulk free-energy barrier associated with the coexisting phases. We also evaluate the long-term correlations in our time series near the finite-size critical points by studying the integrated autocorrelation time τ as a function of the lattice size. This allows us to infer how severe the critical slowing down for this system with long-range interaction and nearby thermodynamic phase transitions is.

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“…3,5 In the limit when the stripe width is much larger than the domain walls, the walls can be approximated by Ising walls and the system can be considered as an Ising system of interacting domain walls. 4 In spite of intense theoretical [3][4][5][6][7][8][9][10][11][12][13][14] and experimental 1,2,[15][16][17] work on the behavior of ultrathin magnetic films, the precise nature of the phases and the relaxational dynamics aspects of these systems is still poorly understood. In Monte Carlo simulations of an Ising model on a square lattice, Booth et al 5 found evidence of a stripe phase at low temperatures, with orientational and positional order reminiscent of the smectic order in liquid crystals.…”

Section: Introductionmentioning

confidence: 99%

Ising nematic phase in ultrathin magnetic films: A Monte Carlo study

et al. 2006

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We study the critical properties of a two-dimensional Ising model with competing ferromagnetic exchange and dipolar interactions, which models an ultrathin magnetic film with high out-of-plane anisotropy in the monolayer limit. We present numerical evidence showing that two different scenarios appear in the model for different values of the exchange to dipolar intensities ratio, namely, a single first-order stripe-tetragonal phase transition or two phase transitions at different temperatures with an intermediate Ising nematic phase between the stripe and the tetragonal ones. Our results are very similar to those predicted by Abanov et al. ͓Phys. Rev. B 51, 1023 ͑1995͔͒, but suggest a much more complex critical behavior than predicted by those authors for both the stripe-nematic and the nematic-tetragonal phase transitions. We also show that the presence of diverging free energy barriers at the stripe-nematic transition makes possible to obtain by slow cooling a metastable supercooled nematic state down to temperatures well below the transition one.

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Metric features of a dipolar model

Cited by 9 publications

References 18 publications

Configurations and observables in an Ising model with heat flow

Configurations and observables in an Ising model with heat flow

Phase transitions and autocorrelation times in two-dimensional Ising model with dipole interactions

Ising nematic phase in ultrathin magnetic films: A Monte Carlo study

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