arXiv:hep-th/9810202 · Journal of Physics A Mathematical and General

On the phase diagram of the discrete Z6spin models

Patrick Dorey, Paolo Provero, Roberto Tateo, S. Vinti

Published Jan 1, 1999• 6 citations

Abstract

We point out some problems with the previously-proposed phase diagram of the $Z_6$ spin models. Consideration of the diagram near to the decoupling surface using both exact and approximate arguments suggests a modification which remedies these deficiencies. With the aid of a new parametrisation of the phase space, we study the models numerically, with results which support our conjectures.

DOI: 10.1088/0305-4470/32/13/002

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arXiv:hep-th/9810202 · Journal of Physics A Mathematical and General

On the phase diagram of the discrete Z6spin models

Patrick Dorey, Paolo Provero, Roberto Tateo, S. Vinti

Published Jan 1, 1999• 6 citations

arXiv HTML PDF

Abstract

We point out some problems with the previously-proposed phase diagram of the

Z_6

spin models. Consideration of the diagram near to the decoupling surface using both exact and approximate arguments suggests a modification which remedies these deficiencies. With the aid of a new parametrisation of the phase space, we study the models numerically, with results which support our conjectures.

DOI: 10.1088/0305-4470/32/13/002

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On the phase diagram of the discrete Z6 spin models

Patrick Dorey, S. Vinti, Paolo Provero +1 more

Jan 1, 19990 citations

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Pál Ruján, Gareth O. Williams, H. L. Frisch +1 more

The phase diagrams of general $q$ -state planar spin models on a square lattice are studied for $q=4\ensuremath{-}7$. The phase diagrams are calculated by a variational method and the infinitesimal Migdal renormalization-group (RG) transformations. Since the Migdal RG commutes with the self-dual transformations of $Z(q)$ models, one expects reliable phase diagrams (but not accurate critical exponents). In fact all exactly known critical points are reproduced by our calculations together with a fair numerical simulation of lines of critical points. Our results clearly indicate the existence of massless phases for $q=6 \mathrm{and} 7$ but are inconclusive for $q=5$ . More accurate methods are needed to determine the phase structure of the $Z(5)$ model; see, for example, the finite-lattice approximation of Roomany and Wyld (preceding paper).The phase diagrams of general $q$-state planar spin models on a square lattice are studied for $q=4\ensuremath{-}7$. The phase diagrams are calculated by a variational method and the infinitesimal Migdal renormalization-group (RG) transformations. Since the Migdal RG commutes with the self-dual transformations of $Z(q)$ models, one expects reliable phase diagrams (but not accurate critical exponents). In fact all exactly known critical points are reproduced by our calculations together with a fair numerical simulation of lines of critical points. Our results clearly indicate the existence of massless phases for $q=6 \mathrm{and} 7$ but are inconclusive for $q=5$. More accurate methods are needed to determine the phase structure of the $Z(5)$ model; see, for example, the finite-lattice approximation of Roomany and Wyld (preceding paper).

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Numerical and analytical studies of several models of correlated electrons are discussed. Based on exact diagonalization and variational Monte Carlo techniques, we have found indications that the two-dimensional t-J model superconducts near phase separation in the regime of quarter-filling density, in agreement with previous results reported by Dagotto and Riera [Phys. Rev. Lett. 70, 682 (1993)]. At this density the dominant channel is ${\mathit{d}}_{\mathit{x}}^{2}$ - ${\mathit{y}}^{2}$ , but a transiton to s-wave superconductivity is observed decreasing the electronic density. In addition, the one-band t-U-V model has also been studied using a mean-field approximation. An interesting region of ${\mathit{d}}_{\mathit{x}}^{2}$ - ${\mathit{y}}^{2}$ superconductivity near phase separation is observed in the phase diagram, and its implications for recent self-consistent studies of d-wave condensates in the context of the high- ${\mathit{T}}_{\mathit{c}}$ cuprates are briefly discussed. Finally, the two-band Hubbard model on a chain is also analyzed. Superconducting correlations near phase separation exist in this model, as it occurs in the t-J model. Based on these nontrivial examples it is conjectured that electronic models tend to have superconducting phases in the vicinity of phase separation, and this regime of parameter space should be explored first when a new model for superconductivity is proposed. Reciprocally, if it is established that a model does not phase separate, even in an extended parameter space, then we believe that its chances of presenting a superconducting phase are considerably reduced.Numerical and analytical studies of several models of correlated electrons are discussed. Based on exact diagonalization and variational Monte Carlo techniques, we have found indications that the two-dimensional t-J model superconducts near phase separation in the regime of quarter-filling density, in agreement with previous results reported by Dagotto and Riera [Phys. Rev. Lett. 70, 682 (1993)]. At this density the dominant channel is ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$, but a transiton to s-wave superconductivity is observed decreasing the electronic density. In addition, the one-band t-U-V model has also been studied using a mean-field approximation. An interesting region of ${\mathit{d}}_{\mathit{x}}^{2}$-${\mathit{y}}^{2}$ superconductivity near phase separation is observed in the phase diagram, and its implications for recent self-consistent studies of d-wave condensates in the context of the high-${\mathit{T}}_{\mathit{c}}$ cuprates are briefly discussed. Finally, the two-band Hubbard model on a chain is also analyzed. Superconducting correlations near phase separation exist in this model, as it occurs in the t-J model. Based on these nontrivial examples it is conjectured that electronic models tend to have superconducting phases in the vicinity of phase separation, and this regime of parameter space should be explored first when a new model for superconductivity is proposed. Reciprocally, if it is established that a model does not phase separate, even in an extended parameter space, then we believe that its chances of presenting a superconducting phase are considerably reduced.

arXiv:cond-mat/9309028Physical review. B, Condensed matterFeb 1, 1994129 citations

We point out some problems with the previously-proposed phase diagram of the

Z_6

The phase diagrams of general

q

-state planar spin models on a square lattice are studied for $q=4\ensuremath{-}7$. The phase diagrams are calculated by a variational method and the infinitesimal Migdal renormalization-group (RG) transformations. Since the Migdal RG commutes with the self-dual transformations of

Z(q)

models, one expects reliable phase diagrams (but not accurate critical exponents). In fact all exactly known critical points are reproduced by our calculations together with a fair numerical simulation of lines of critical points. Our results clearly indicate the existence of massless phases for

q=6 \mathrm{and} 7

but are inconclusive for

q=5

. More accurate methods are needed to determine the phase structure of the

Z(5)

model; see, for example, the finite-lattice approximation of Roomany and Wyld (preceding paper).

We investigate the symmetric Ashkin-Teller (AT) model on the triangular lattice in the antiferromagnetic two-spin coupling region (

J 0

, with K the four-spin interaction. Further, we find that, in the

J \rightarrow -\infty

limit, the critical line terminates at the decoupled point

K=0

. From the numerical results and the exact mapping, we conjecture that this `tricritical' point (

J \rightarrow -\infty, K=0

) is Berezinsky-Kosterlitz-Thouless-like and the logarithmic correction is absent. The dynamic critical exponent of the worm algorithm is estimated as

z=0.28(1)

near

(J \rightarrow -\infty, K=0)

{\mathit{d}}_{\mathit{x}}^{2}

{\mathit{y}}^{2}

, but a transiton to s-wave superconductivity is observed decreasing the electronic density. In addition, the one-band t-U-V model has also been studied using a mean-field approximation. An interesting region of

{\mathit{d}}_{\mathit{x}}^{2}

{\mathit{y}}^{2}

superconductivity near phase separation is observed in the phase diagram, and its implications for recent self-consistent studies of d-wave condensates in the context of the high-

{\mathit{T}}_{\mathit{c}}

cuprates are briefly discussed. Finally, the two-band Hubbard model on a chain is also analyzed. Superconducting correlations near phase separation exist in this model, as it occurs in the t-J model. Based on these nontrivial examples it is conjectured that electronic models tend to have superconducting phases in the vicinity of phase separation, and this regime of parameter space should be explored first when a new model for superconductivity is proposed. Reciprocally, if it is established that a model does not phase separate, even in an extended parameter space, then we believe that its chances of presenting a superconducting phase are considerably reduced.