Journal of Physics Conference Series

Exact calculations for the ground state properties of the frustrated 2-dimensional Ising model

John A. Blackman, J. Poulter

Published Feb 28, 2006• 0 citations

Abstract

We have developed a technique that enables the exact calculation of the ground state properties of the 2-dimensional ±J Ising model. This paper gives an overview of the methodology and describes the latest results on the correlation function.

DOI: 10.1088/1742-6596/30/1/017

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Journal of Physics Conference Series

Exact calculations for the ground state properties of the frustrated 2-dimensional Ising model

John A. Blackman, J. Poulter

Published Feb 28, 2006• 0 citations

Publisher

Abstract

DOI: 10.1088/1742-6596/30/1/017

Related papers

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之康尾関, Yukiyasu Ozeki

Jan 1, 19900 citations

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Gabor Forgács

The spin-spin correlation function in the ground state of some two-dimensional fully frustrated spin models are investigated. The correlations are long ranged and decay as $\frac{1}{{r}^{\ensuremath{\eta}}}$, where $r$ is the distance between the two spins and $\ensuremath{\eta}=\frac{1}{2}$. This result is true for both the square and triangular fully frustrated lattices, thus suggesting that these models form a universality class. It is shown that the fully frustrated Ising model on a square lattice can be mapped exactly into a special Baxter model. The spin-spin correlation function of this Baxter model can be calculated exactly. The ground state of the fully frustrated square Ising model corresponds to the free fermion point of the $F$ model and therefore, through duality, to the decoupling point of the critical Baxter line. The relationship between the $F$ model above the critical temperature and the Gaussian model above the multicritical point is discussed.The spin-spin correlation function in the ground state of some two-dimensional fully frustrated spin models are investigated. The correlations are long ranged and decay as $\frac{1}{{r}^{\ensuremath{\eta}}}$, where $r$ is the distance between the two spins and $\ensuremath{\eta}=\frac{1}{2}$. This result is true for both the square and triangular fully frustrated lattices, thus suggesting that these models form a universality class. It is shown that the fully frustrated Ising model on a square lattice can be mapped exactly into a special Baxter model. The spin-spin correlation function of this Baxter model can be calculated exactly. The ground state of the fully frustrated square Ising model corresponds to the free fermion point of the $F$ model and therefore, through duality, to the decoupling point of the critical Baxter line. The relationship between the $F$ model above the critical temperature and the Gaussian model above the multicritical point is discussed.

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Ingo Peschel

The European Physical Journal BDec 1, 198219 citations

r

is the distance between the two spins and $\ensuremath{\eta}=\frac{1}{2}$. This result is true for both the square and triangular fully frustrated lattices, thus suggesting that these models form a universality class. It is shown that the fully frustrated Ising model on a square lattice can be mapped exactly into a special Baxter model. The spin-spin correlation function of this Baxter model can be calculated exactly. The ground state of the fully frustrated square Ising model corresponds to the free fermion point of the

F

model and therefore, through duality, to the decoupling point of the critical Baxter line. The relationship between the

F

model above the critical temperature and the Gaussian model above the multicritical point is discussed.

{I}_{h}

, and water ice

{I}_{c}

. In addition, we show that these systems are in a Coulomb phase by computing the dipolar form of the correlation functions. As a further benchmark of our methods, we calculate the critical temperature and exponents of the Ising model on the cubic lattice.

We have found the exact ground state for two frustrated quantum spin-

\frac{1}{2}

models on a linear chain. The first model describes the antiferromagnet-ferromagnet transition point. The singlet state at this point has double-spiral ordering. The second model is equivalent to special case of the spin-

\frac{1}{2}

ladder. It has a nondegenerate singlet ground state with exponentially decaying spin correlations, and there is an energy gap. The exact ground-state wave function of these models is presented in a special recurrent form, and a recurrence technique for expectation value calculations is developed.