Physical Review Letters

N -Color Ashkin-Teller Model in Two Dimensions: Solution in the Large- N Limit

Eduardo Fradkin

Published Nov 19, 1984• 45 citations

Abstract

The $N$-color Ashkin-Teller model is solved exactly in the large-$N$ limit in two dimensions. The phase diagram is found. It is shown that for positive four-spin coupling the transition is first order while for negative four-spin coupling the transition is continuous and Ising type. The specific heat near the second-order transition is calculated and it is found to be finite at the transition because of large corrections to scaling. The latent heat and correlation length at the first-order transition are also calculated.

DOI: 10.1103/physrevlett.53.1967

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Physical Review Letters

N -Color Ashkin-Teller Model in Two Dimensions: Solution in the Large- N Limit

Eduardo Fradkin

Published Nov 19, 1984• 45 citations

Publisher

Abstract

The

N

-color Ashkin-Teller model is solved exactly in the large-

N

limit in two dimensions. The phase diagram is found. It is shown that for positive four-spin coupling the transition is first order while for negative four-spin coupling the transition is continuous and Ising type. The specific heat near the second-order transition is calculated and it is found to be finite at the transition because of large corrections to scaling. The latent heat and correlation length at the first-order transition are also calculated.

DOI: 10.1103/physrevlett.53.1967

Related papers

Large-Nlimit of theXY-Ashkin-Teller model: solution in two dimensions

Giuseppe Gonnella, A. Lamura

Journal of Physics A Mathematical and GeneralJul 29, 19990 citations

N -color Ashkin-Teller model

Gary S. Grest, Michael Widom

We study a model Hamiltonian consisting of $N$ Ising models coupled pairwise through a four-spin interaction ${K}_{4}$ . When $N=2$ this model is the well-known Ashkin-Teller model which shows nonuniversal critical behavior in two dimensions in the neighborhood of ${K}_{4}=0$ . To see if this behavior persists for $N\ensuremath{\ne}2$ we perform a first-order-perturbation expansion around the decoupling point in two dimensions. As an aid in interpreting the results of this perturbation expansion we have determined the phase diagram of the system through mean-field theory and Monte Carlo studies in both two and three dimensions for $N=3$ . The results show that $N=2$ is special because the coupling between Ising models is marginal over a range of values of ${K}_{4}$ . We discuss the effect of the coupling ${K}_{4}$ for $N\ensuremath{\ne}2$.We study a model Hamiltonian consisting of $N$ Ising models coupled pairwise through a four-spin interaction ${K}_{4}$. When $N=2$ this model is the well-known Ashkin-Teller model which shows nonuniversal critical behavior in two dimensions in the neighborhood of ${K}_{4}=0$. To see if this behavior persists for $N\ensuremath{\ne}2$ we perform a first-order-perturbation expansion around the decoupling point in two dimensions. As an aid in interpreting the results of this perturbation expansion we have determined the phase diagram of the system through mean-field theory and Monte Carlo studies in both two and three dimensions for $N=3$. The results show that $N=2$ is special because the coupling between Ising models is marginal over a range of values of ${K}_{4}$. We discuss the effect of the coupling ${K}_{4}$ for $N\ensuremath{\ne}2$.

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Hatem Barghathi, Fawaz Y. Hrahsheh, José A. Hoyos +2 more

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Youssef Makoudi, Gesualdo Delfino A

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M. Badehdah, Smain Bekhechi, A. Benyoussef +1 more

Two nonperturbative methods by means of the transfer-matrix finite-size-scaling and Monte Carlo simulations are used to investigate the spin-1 Ashkin-Teller model (ATM). We have obtained rich phase diagrams with first- and second-order phase transitions with several multicritical points of higher order. Also this model exhibits a partially ordered phase ${\mathrm{PO}}_{2}$ which does not exist in the spin-1/2 Ashkin-Teller model (ATM). Finally, the critical behavior of this model is discussed.Two nonperturbative methods by means of the transfer-matrix finite-size-scaling and Monte Carlo simulations are used to investigate the spin-1 Ashkin-Teller model (ATM). We have obtained rich phase diagrams with first- and second-order phase transitions with several multicritical points of higher order. Also this model exhibits a partially ordered phase ${\mathrm{PO}}_{2}$ which does not exist in the spin-1/2 Ashkin-Teller model (ATM). Finally, the critical behavior of this model is discussed.

Physical review. B, Condensed matterMar 1, 199915 citations

Critical behavior of the N -component Ashkin-Teller model with bond impurities

Ganpathy N. Murthy

The $N$ -component Ashkin-Teller model is a system of $N$ Ising models coupled by a four-spin interaction. The continuum limit of this model is the $\mathrm{O}(N)$ Gross-Neveu model. In this report the critical behavior of the model with weak bond impurities is derived from a renormalization-group analysis. It is found that quenched randomness converts a first-order transition into a second-order transition.The $N$-component Ashkin-Teller model is a system of $N$ Ising models coupled by a four-spin interaction. The continuum limit of this model is the $\mathrm{O}(N)$ Gross-Neveu model. In this report the critical behavior of the model with weak bond impurities is derived from a renormalization-group analysis. It is found that quenched randomness converts a first-order transition into a second-order transition.

Physical review. B, Condensed matterNov 1, 198713 citations

The

N

-color Ashkin-Teller model is solved exactly in the large-

N

We study a model Hamiltonian consisting of

N

Ising models coupled pairwise through a four-spin interaction

{K}_{4}

. When

N=2

this model is the well-known Ashkin-Teller model which shows nonuniversal critical behavior in two dimensions in the neighborhood of

{K}_{4}=0

. To see if this behavior persists for $N\ensuremath{\ne}2$ we perform a first-order-perturbation expansion around the decoupling point in two dimensions. As an aid in interpreting the results of this perturbation expansion we have determined the phase diagram of the system through mean-field theory and Monte Carlo studies in both two and three dimensions for

N=3

. The results show that

N=2

is special because the coupling between Ising models is marginal over a range of values of

{K}_{4}

. We discuss the effect of the coupling

{K}_{4}

for $N\ensuremath{\ne}2$.

{\mathrm{PO}}_{2}

which does not exist in the spin-1/2 Ashkin-Teller model (ATM). Finally, the critical behavior of this model is discussed.

The

N

-component Ashkin-Teller model is a system of

N

Ising models coupled by a four-spin interaction. The continuum limit of this model is the

\mathrm{O}(N)

Gross-Neveu model. In this report the critical behavior of the model with weak bond impurities is derived from a renormalization-group analysis. It is found that quenched randomness converts a first-order transition into a second-order transition.