We predict the locations of several multicritical points of the Potts spin glass model on the triangular lattice. In particular, continuous multicritical lines, which consist of multicritical points, are obtained for two types of two-state Potts (i.e., Ising) spin glasses with two- and three-body interactions on the triangular lattice. These results provide us with numerous examples to further verify the validity of the conjecture, which has succeeded in deriving highly precise locations of multicritical points for several spin glass models. The technique, called the direct triangular duality, a variant of the ordinary duality transformation, directly relates the triangular lattice with its dual triangular lattice in conjunction with the replica method.We predict the locations of several multicritical points of the Potts spin glass model on the triangular lattice. In particular, continuous multicritical lines, which consist of multicritical points, are obtained for two types of two-state Potts (i.e., Ising) spin glasses with two- and three-body interactions on the triangular lattice. These results provide us with numerous examples to further verify the validity of the conjecture, which has succeeded in deriving highly precise locations of multicritical points for several spin glass models. The technique, called the direct triangular duality, a variant of the ordinary duality transformation, directly relates the triangular lattice with its dual triangular lattice in conjunction with the replica method.

arXiv:0706.2052Journal of the Physical Society of JapanOct 24, 20073 citations

Location and properties of the multicritical point in the Gaussian and ± J Ising spin glasses

S. L. A. de Queiroz

We use transfer-matrix and finite-size scaling methods to investigate the location and properties of the multicritical point of two-dimensional Ising spin glasses on square, triangular, and honeycomb lattices with both binary and Gaussian disorder distributions. For square and triangular lattices with binary disorder, the estimated position of the multicritical point is in numerical agreement with recent conjectures regarding its exact location. For the remaining four cases, our results indicate disagreement with the respective versions of the conjecture, though by very small amounts, never exceeding 0.2%. Our results for (i) the correlation-length exponent $\ensuremath{\nu}$ governing the ferroparamagnetic transition, (ii) the critical domain-wall energy amplitude $\ensuremath{\eta}$, (iii) the conformal anomaly $c$ , (iv) the finite-size susceptibility exponent $\ensuremath{\gamma}/\ensuremath{\nu}$, and (v) the set of multifractal exponents ${{\ensuremath{\eta}}_{k}}$ associated to the moments of the probability distribution of spin-spin correlation functions at the multicritical point are consistent with universality as regards lattice structure and disorder distribution and in good agreement with existing estimates.We use transfer-matrix and finite-size scaling methods to investigate the location and properties of the multicritical point of two-dimensional Ising spin glasses on square, triangular, and honeycomb lattices with both binary and Gaussian disorder distributions. For square and triangular lattices with binary disorder, the estimated position of the multicritical point is in numerical agreement with recent conjectures regarding its exact location. For the remaining four cases, our results indicate disagreement with the respective versions of the conjecture, though by very small amounts, never exceeding 0.2%. Our results for (i) the correlation-length exponent $\ensuremath{\nu}$ governing the ferroparamagnetic transition, (ii) the critical domain-wall energy amplitude $\ensuremath{\eta}$, (iii) the conformal anomaly $c$, (iv) the finite-size susceptibility exponent $\ensuremath{\gamma}/\ensuremath{\nu}$, and (v) the set of multifractal exponents ${{\ensuremath{\eta}}_{k}}$ associated to the moments of the probability distribution of spin-spin correlation functions at the multicritical point are consistent with universality as regards lattice structure and disorder distribution and in good agreement with existing estimates.

arXiv:0902.4153Physical Review BMay 7, 200927 citations

POSSIBLY EXACT SOLUTION FOR THE MULTICRITICAL POINT OF FINITE-DIMENSIONAL SPIN GLASSES

Hidetoshi Nishimori, Koujin Takeda, Tomohiro Sasamoto

Recent Progress in Many-Body TheoriesJul 1, 20060 citations

c

, (iv) the finite-size susceptibility exponent $\ensuremath{\gamma}/\ensuremath{\nu}$, and (v) the set of multifractal exponents ${{\ensuremath{\eta}}_{k}}$ associated to the moments of the probability distribution of spin-spin correlation functions at the multicritical point are consistent with universality as regards lattice structure and disorder distribution and in good agreement with existing estimates.