It is shown that (i) the N-component Ashkin-Teller model in d=2 has continuous O(N) symmetry, (ii) its critical properties near the decoupled Ising transition are determined by the massive Gross-Neveu [(\ensuremath{\psi}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\psi} ${)}^{2}$ ] model in general and the (integrable) massless version along a line, (iii) the known results for the massless Gross-Neveu model imply that the first-order transition found as N\ensuremath{\rightarrow}\ensuremath{\infty} persists down to N=3 along this line, (iv) the supersymmetry of the N=3 model implies that the leading singularity of the free energy is zero along the first-order line, and (v) the N=4 model along this line decouples into two identical N=2 models up to subleading corrections.It is shown that (i) the N-component Ashkin-Teller model in d=2 has continuous O(N) symmetry, (ii) its critical properties near the decoupled Ising transition are determined by the massive Gross-Neveu [(\ensuremath{\psi}\ifmmode\bar\else\textasciimacron\fi{}\ensuremath{\psi}${)}^{2}$] model in general and the (integrable) massless version along a line, (iii) the known results for the massless Gross-Neveu model imply that the first-order transition found as N\ensuremath{\rightarrow}\ensuremath{\infty} persists down to N=3 along this line, (iv) the supersymmetry of the N=3 model implies that the leading singularity of the free energy is zero along the first-order line, and (v) the N=4 model along this line decouples into two identical N=2 models up to subleading corrections.

Physical Review LettersJul 29, 198552 citations

On critical properties of the Ashkin-Teller model

Chungpeng Fan

Physics Letters AApr 1, 1972107 citations

The anisotropic Ashkin–Teller model: a renormalization group study

Claudionor Gomes Bezerra, Ananias M. Mariz, João Medeiros de Araújo +1 more

arXiv:cond-mat/0102080Physica A Statistical Mechanics and its ApplicationsMar 1, 200111 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

{)}^{2}

] model in general and the (integrable) massless version along a line, (iii) the known results for the massless Gross-Neveu model imply that the first-order transition found as N\ensuremath{\rightarrow}\ensuremath{\infty} persists down to N=3 along this line, (iv) the supersymmetry of the N=3 model implies that the leading singularity of the free energy is zero along the first-order line, and (v) the N=4 model along this line decouples into two identical N=2 models up to subleading corrections.

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.