Dynamic critical exponent 
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 of the three-dimensional Ising universality class: Monte Carlo simulations of the improved Blume-Capel model

Hasenbusch, Martin

doi:10.1103/physreve.101.022126

Cited by 28 publications

(13 citation statements)

References 61 publications

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“…We believe this is the first work to obtain the dynamic critical exponents θ and z for the majority-vote model in threedimensional regular lattices. Nevertheless, our findings are very close to z = 2.03(4) 52 , z = 2.0245(15) 53 , and θ = 0.108(2) 54 from simulations of the three-dimensional Ising model. Therefore, the majority-vote model in threedimensions belongs to the three-dimensional Ising universality class.…”

Section: Discussionsupporting

confidence: 84%

Short-time Monte Carlo simulation of the majority-vote model on cubic lattices

Nascimento,

de Souza,

Vilela

et al. 2020

Preprint

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We perform short-time Monte Carlo simulations to study the criticality of the isotropic twostate majority-vote model on cubic lattices of volume N = L 3 , with L up to 2048. We obtain the precise location of the critical point by examining the scaling properties of a new auxiliary function Ψ. We perform finite-time scaling analysis to accurately calculate the whole set of critical exponents, including the dynamical critical exponent z = 2.027(9), and the initial slip exponent θ = 0.1081(1). Our results indicate that the majority-vote model in three dimensions belongs to the same universality class of the three-dimensional Ising model.

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Section: Discussionsupporting

confidence: 84%

Short-time Monte Carlo simulation of the majority-vote model on cubic lattices

Nascimento,

de Souza,

Vilela

et al. 2020

Preprint

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“…For comparison, this is larger than the dynamical exponent for spin flip dynamics in the 3D Ising model [79][80][81][82][83][84][85][86][87][88][89][90][91][92], for which a recent estimate is z = 2.0245(15) [92].…”

Section: B Dynamical Scaling Collapsementioning

confidence: 82%

“…VIII C below). This is analogous to, say, the critical 3D Ising model which shows a robust universality class for spin-flip dynamics with no conservation laws (the universality class of "Model A" [77][78][79][80][81][82][83][84][85][86][87][88][89][90][91][92]).…”

Section: A Universal Dynamics and Dualitymentioning

confidence: 99%

Self-dual criticality in three-dimensional $\mathbb{Z}_2$ gauge theory with matter

Somoza,

Serna,

Nahum

2020

Preprint

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The simplest topologically ordered phase in 2+1D is the deconfined phase of Z2 gauge theory, realized for example in the toric code. This phase permits a duality that exchanges electric and magnetic excitations ("e" and "m" particles). Condensing either particle while the other remains gapped yields a phase transition with 3D Ising exponents. More mysterious, however, is the transition out of the deconfined phase when self-duality symmetry is preserved. If this transition is continuous, which has so far been unclear, then it may be the simplest critical point for which we still lack any useful continuum Lagrangian description. This transition also has a soft matter interpretation, as a multicritical point for classical membranes in 3D.We study the self-dual transition with Monte Carlo simulations of the Z2 gauge-Higgs model on cubic lattices of linear size L ≤ 96. Our results indicate a continuous transition: for example, cumulants show a striking parameter-free scaling collapse. We estimate scaling dimensions by using duality symmetry to distinguish the leading duality-odd/duality-even scaling operators A and S. All local operators have large scaling dimensions, making standard techniques for locating the critical point ineffective. We develop an alternative using "renormalization group trajectories" of cumulants. We check that two-and three-point functions, and temporal correlators in the Monte-Carlo dynamics, are scale-invariant, with scaling dimensions xA and xS and dynamical exponent z.We also give a picture for emergence of 1-form symmetries, in some parts of the phase diagram, in terms of "patching" of membranes/worldsurfaces. We relate this to the percolation of anyon worldlines in spacetime. Analyzing percolation yields a fourth exponent for the self-dual transition. We propose variations of the model for further investigation.

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“…Its estimated value for various dimensions and N = 1 (the Ising model) is shown in table 1. For a recent calulation, see [39]. For the range of fractal dimensions D that is relevant for us, 2 ≤ D ≤ 3.5, we use the formula z = 2 + c • η [13], where we approximate c ≈ 2/3.…”

Section: Lattice Gas Model Of Financial Marketsmentioning

confidence: 99%

Financial Markets and the Phase Transition between Water and Steam

Schmidhuber

2021

Preprint

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A lattice gas model of financial markets is presented that has the potential to explain previous empirical observations of the interplay of trends and reversion in the markets, including a Langevin equation for the time evolution of trends. In this model, the shares of an asset correspond to gas molecules that are distributed across a hidden social network of investors. Neighbors in the network tend to align their positions due to herding behavior, corresponding to an attractive force of the gas molecules.This model is equivalent to the Ising model on this network, with the magnetization in the role of the deviation of the market price of an asset from its long-term value. In efficient markets, it is argued that the system is driven to its critical temperature, where it undergoes a second-order phase transition. There, it is characterized by long-range correlations and universal critical exponents, in analogy with the phase transition between water and steam.Applying scalar field theory and the renormalization group, we show that these critical exponents imply predictions for the auto-correlations of financial market returns. For a network topology of R D , consistency with observation implies a fractal dimension of the network of D ≈ 3.3, and a correlation time of 10 years. However, while this simplest model agrees well with market data on long time scales, it does not explain the observed market trends over time horizons from one month to one year.In a next step, the approach should therefore be extended to the vicinity of the critical point, to other models of critical dynamics, and to general network topologies.It allows us to indirectly measure universal properties of the hidden social network of investors from the empirically observable interplay of trends and reversion.

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Dynamic critical exponent z of the three-dimensional Ising universality class: Monte Carlo simulations of the improved Blume-Capel model

Cited by 28 publications

References 61 publications

Short-time Monte Carlo simulation of the majority-vote model on cubic lattices

Short-time Monte Carlo simulation of the majority-vote model on cubic lattices

Self-dual criticality in three-dimensional $\mathbb{Z}_2$ gauge theory with matter

Financial Markets and the Phase Transition between Water and Steam

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