Order parameter critical exponent of the directed Ising universality class in one dimension

Su‐Chan Park

Published Feb 8, 2020• 0 citations

Abstract

Via extensive Monte Carlo simulations along with systematic analyses of corrections to scaling, we estimate the order parameter critical exponent $\beta$ of the directed Ising universality class. The value of $\beta$ was conjectured to be $\frac{13}{14}$ and Monte Carlo simulation studies in the literature have repeatedly reproduced the consistent values to the conjecture. In this paper, however, we find that the conjectured value of $\beta$ is not correct. Rather, we obtain $\beta$ = 1.020(5) from different models belonging to the directed Ising class.

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Order parameter critical exponent of the directed Ising universality class in one dimension

Su‐Chan Park

Published Feb 8, 2020• 0 citations

OpenAlex

Abstract

Via extensive Monte Carlo simulations along with systematic analyses of corrections to scaling, we estimate the order parameter critical exponent

\beta

of the directed Ising universality class. The value of

\beta

was conjectured to be

\frac{13}{14}

and Monte Carlo simulation studies in the literature have repeatedly reproduced the consistent values to the conjecture. In this paper, however, we find that the conjectured value of

\beta

is not correct. Rather, we obtain

\beta

= 1.020(5) from different models belonging to the directed Ising class.

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arXiv:1402.1991Feb 9, 20141 citation

Via extensive Monte Carlo simulations along with systematic analyses of corrections to scaling, we estimate the order parameter critical exponent

\beta

of the directed Ising universality class. The value of

\beta

was conjectured to be

\frac{13}{14}

and Monte Carlo simulation studies in the literature have repeatedly reproduced the consistent values to the conjecture. In this paper, however, we find that the conjectured value of

\beta

is not correct. Rather, we obtain

\beta

= 1.020(5) from different models belonging to the directed Ising class.

ϵ

-expansion techniques, and resummed perturbation theory.

β_c

, critical exponents, and critical values of a number of dimensionless parameters. Independent estimates are obtained for

β_c

and the exponent

ν

from thermodynamic derivative peak data. A detailed explanation is given of scaling in the thermodynamic limit with the ISG scaling variable

τ= 1-β^2/β_c^2

and the appropriate scaling expressions. Data over the entire paramagnetic range of temperatures are analysed in order to obtain further estimates of the critical exponents together with correction to scaling terms. The Privman-Fisher ansatz then leads to compact scaling expressions for the whole paramagnetic regime and for all sample sizes L. Comparisons between the 4d ISG models show that the critical dimensionless parameters characteristic of a universality class, and the susceptibility and correlation length critical exponents

γ

and

ν

, depend on the form of the interaction distribution. From these observations it can be deduced that critical exponents are not universal in ISGs, at least in dimension four.