A two-dimensional $n$ -component spin model with cubic or isotropic symmetry is mapped onto a solid-on-solid model. Subject to some plausible assumptions this leads to an analytic calculation of the critical point and some critical indices for $\ensuremath{-}2<~n<~2$.A two-dimensional $n$-component spin model with cubic or isotropic symmetry is mapped onto a solid-on-solid model. Subject to some plausible assumptions this leads to an analytic calculation of the critical point and some critical indices for $\ensuremath{-}2<~n<~2$.

Physical Review LettersOct 11, 19821,010 citations

Extraordinary transition in the two-dimensional O(n) model

Murray T. Batchelor, John Cardy

arXiv:cond-mat/9705238Nuclear Physics BDec 1, 19978 citations

Kadanoff block transformation by the Monte Carlo technique

Zvi Friedman, J. Felsteiner

A program combining the Monte Carlo technique and the Kadanoff block transformation is carried out for the Ising model in two and three dimensions, and the critical point and the critical indices $\ensuremath{\nu}$ and $\ensuremath{\delta}$ are obtained. A sequence of approximations seems to converge to the exact Onsager result in two dimensions, although the convergence of $\ensuremath{\nu}$ is rather slow. In three dimensions, the numbers obtained seem to tend towards the results from exact series expansions.A program combining the Monte Carlo technique and the Kadanoff block transformation is carried out for the Ising model in two and three dimensions, and the critical point and the critical indices $\ensuremath{\nu}$ and $\ensuremath{\delta}$ are obtained. A sequence of approximations seems to converge to the exact Onsager result in two dimensions, although the convergence of $\ensuremath{\nu}$ is rather slow. In three dimensions, the numbers obtained seem to tend towards the results from exact series expansions.

Physical review. B, Solid stateJun 1, 197742 citations

PHASE TRANSITIONS IN THE TWO-DIMENSIONAL O(3) MODEL

Henk W. J. Blöte, Wenan Guo

APCTP-Nankai Joint Symposium on Lattice Statistics and Mathematical PhysicsNov 1, 20020 citations

Renormalization-group study of the crossover to classical behavior for an Ising model with vacancies

J.J.M. Rijpkema

By using Kadanoff's variational renormalization-group method an Ising model with vacancies is investigated for dimensions up to $d=4$ to study the crossover to classical behavior. Up to a crossover dimension $d\ensuremath{\simeq}3.4$, both an optimal critical and tricritical fixed point are located with critical indices that agree well with other data. At $d\ensuremath{\simeq}3.4$, both fixed points merge, representing in this way the crossover to classical behavior. At $d>3.4$ , indications are found that the two fixed points do not annihilate but form a "marginal" pair that describes both critical and tricritical behavior.By using Kadanoff's variational renormalization-group method an Ising model with vacancies is investigated for dimensions up to $d=4$ to study the crossover to classical behavior. Up to a crossover dimension $d\ensuremath{\simeq}3.4$, both an optimal critical and tricritical fixed point are located with critical indices that agree well with other data. At $d\ensuremath{\simeq}3.4$, both fixed points merge, representing in this way the crossover to classical behavior. At $d>3.4$, indications are found that the two fixed points do not annihilate but form a "marginal" pair that describes both critical and tricritical behavior.

Physical Review AFeb 1, 19843 citations

A two-dimensional

n

-component spin model with cubic or isotropic symmetry is mapped onto a solid-on-solid model. Subject to some plausible assumptions this leads to an analytic calculation of the critical point and some critical indices for $\ensuremath{-}2<~n<~2$.

By using Kadanoff's variational renormalization-group method an Ising model with vacancies is investigated for dimensions up to

d=4

to study the crossover to classical behavior. Up to a crossover dimension $d\ensuremath{\simeq}3.4$, both an optimal critical and tricritical fixed point are located with critical indices that agree well with other data. At $d\ensuremath{\simeq}3.4$, both fixed points merge, representing in this way the crossover to classical behavior. At

d>3.4

, indications are found that the two fixed points do not annihilate but form a "marginal" pair that describes both critical and tricritical behavior.