The Blume-Capel universality class

We study the Blume-Capel universality class in $d=\frac{10}{3}\ensuremath{-}\ensuremath{\epsilon}$ dimensions. The renormalization group flow is extracted by looking at poles in fractional dimension of three loop diagrams using $\overline{\mathrm{MS}}$ . The theory is the only nontrivial universality class which admits an expansion to three dimensions with $\ensuremath{\epsilon}=\frac{1}{3}<1$. We compute the relevant scaling exponents and estimate some of the operator product expansion coefficients to the leading order. Our findings agree with and complement conformal field theory results. Finally we discuss a family of nonunitary multicritical models which includes the Lee-Yang and Blume-Capel classes as special cases.We study the Blume-Capel universality class in $d=\frac{10}{3}\ensuremath{-}\ensuremath{\epsilon}$ dimensions. The renormalization group flow is extracted by looking at poles in fractional dimension of three loop diagrams using $\overline{\mathrm{MS}}$. The theory is the only nontrivial universality class which admits an expansion to three dimensions with $\ensuremath{\epsilon}=\frac{1}{3}<1$. We compute the relevant scaling exponents and estimate some of the operator product expansion coefficients to the leading order. Our findings agree with and complement conformal field theory results. Finally we discuss a family of nonunitary multicritical models which includes the Lee-Yang and Blume-Capel classes as special cases.

arXiv:1706.06887Physical review. D/Physical review. D.Oct 2, 201727 citations

The Kosterlitz-Thouless universality class

R. Kenna, A.C. Irving

arXiv:hep-lat/9601029Nuclear Physics BFeb 1, 199752 citations

Static universality of the Ising and Blume–Capel models on two-dimensional Penrose tiles

Mouhcine Azhari, Unjong Yu

We study the phase transitions and the critical behavior of the Ising and Blume–Capel models on two kinds of two-dimensional Penrose tiles employing Monte Carlo methods and detailed finite-size scaling analysis. The Wolff algorithm is used for the Ising model whereas the Wang–Landau and Metropolis algorithms are used for the Blume–Capel model to obtain critical temperatures and exponents. The phase diagram of the Blume–Capel model reveals the presence of the double transition, the reentrant behavior, and the tricriticality in the vicinity of the critical single-ion anisotropy. Our results indicate that continuous phase transitions of the Ising and Blume–Capel models on the Penrose tiles belong to the two-dimensional Ising universality class. However, the scaling functions depend on the spin magnitude, anisotropy, and graph shape. Lastly, we verify that the critical Binder cumulant is also universal but depends on the shape of the graph.We study the phase transitions and the critical behavior of the Ising and Blume–Capel models on two kinds of two-dimensional Penrose tiles employing Monte Carlo methods and detailed finite-size scaling analysis. The Wolff algorithm is used for the Ising model whereas the Wang–Landau and Metropolis algorithms are used for the Blume–Capel model to obtain critical temperatures and exponents. The phase diagram of the Blume–Capel model reveals the presence of the double transition, the reentrant behavior, and the tricriticality in the vicinity of the critical single-ion anisotropy. Our results indicate that continuous phase transitions of the Ising and Blume–Capel models on the Penrose tiles belong to the two-dimensional Ising universality class. However, the scaling functions depend on the spin magnitude, anisotropy, and graph shape. Lastly, we verify that the critical Binder cumulant is also universal but depends on the shape of the graph.

Results in PhysicsJun 16, 20235 citations

Metastability of Universality Classes

WORLD SCIENTIFIC eBooksSep 11, 20180 citations

Local persistense and blocking in the two dimensional Blume-Capel Model

Roberto da Silva, Sílvio R. Dahmen

In this letter we study the local persistence of the two--dimensional Blume-- Capel Model by extension of the concept of Glauber dynamics. We verify that for any value of the ratio $α=D/J$ between anisotropy $D$ and exchange $J$ the persistence shows a power law behavior. In particular for $α<0$ we find a persistence exponent $θ_{l}=0.2096(13)$ , \textit{i.e.} in the Ising universality class. For $α>0$ ( $α\neq 1$ ) we observe the occurrence of blocking.In this letter we study the local persistence of the two--dimensional Blume-- Capel Model by extension of the concept of Glauber dynamics. We verify that for any value of the ratio $α=D/J$ between anisotropy $D$ and exchange $J$ the persistence shows a power law behavior. In particular for $α<0$ we find a persistence exponent $θ_{l}=0.2096(13)$, \textit{i.e.} in the Ising universality class. For $α>0$ ($α\neq 1$) we observe the occurrence of blocking.

arXiv:cond-mat/0404082Apr 4, 20040 citations

\overline{\mathrm{MS}}

. The theory is the only nontrivial universality class which admits an expansion to three dimensions with $\ensuremath{\epsilon}=\frac{1}{3}<1$. We compute the relevant scaling exponents and estimate some of the operator product expansion coefficients to the leading order. Our findings agree with and complement conformal field theory results. Finally we discuss a family of nonunitary multicritical models which includes the Lee-Yang and Blume-Capel classes as special cases.

In this letter we study the local persistence of the two--dimensional Blume-- Capel Model by extension of the concept of Glauber dynamics. We verify that for any value of the ratio

α=D/J

between anisotropy

D

and exchange

J

the persistence shows a power law behavior. In particular for

α<0

we find a persistence exponent

θ_{l}=0.2096(13)

, \textit{i.e.} in the Ising universality class. For

α>0

(

α\neq 1

) we observe the occurrence of blocking.