Phase Diagrams, Criticality, and Local Properties of Spin Glasses and Random-Field Ising Models from Renormalization - Calculations.

An Ising model including field randomness and $\ifmmode\pm\else\textpm\fi{}J$ bond randomness is studied by renormalization-group theory in spatial dimensions $d=2$ and 3. In $d=3,$ with field randomness but no $\ifmmode\pm\else\textpm\fi{}J$ randomness, ferromagnetic and paramagnetic phases occur with no intervening spin-glass phase. Also in $d=3,$ at sufficient $\ifmmode\pm\else\textpm\fi{}J$ randomness, a spin-glass phase occurs, but is replaced by the paramagnetic phase for any nonzero random field, also implying its disappearance for any nonzero uniform field. In $d=2,$ no ferromagnetic phase under random fields and no spin-glass phase occur. Global phase diagrams uniting the random-field and spin-glass problems are evaluated. The strong violation of critical phenomena universality, previously found adjoining random-bond tricriticality in $d=3,$ is seen here in $d=2.$ An Ising model including field randomness and $\ifmmode\pm\else\textpm\fi{}J$ bond randomness is studied by renormalization-group theory in spatial dimensions $d=2$ and 3. In $d=3,$ with field randomness but no $\ifmmode\pm\else\textpm\fi{}J$ randomness, ferromagnetic and paramagnetic phases occur with no intervening spin-glass phase. Also in $d=3,$ at sufficient $\ifmmode\pm\else\textpm\fi{}J$ randomness, a spin-glass phase occurs, but is replaced by the paramagnetic phase for any nonzero random field, also implying its disappearance for any nonzero uniform field. In $d=2,$ no ferromagnetic phase under random fields and no spin-glass phase occur. Global phase diagrams uniting the random-field and spin-glass problems are evaluated. The strong violation of critical phenomena universality, previously found adjoining random-bond tricriticality in $d=3,$ is seen here in $d=2.$

APSMar 1, 19970 citations

The phase diagram of Ising spin glasses

Ian A. Campbell, L. de Arcangelis

Journal of Magnetism and Magnetic MaterialsFeb 1, 19920 citations

Renormalization group solution of Ising spin models

Michael Nauenberg

Springer eBooksApr 6, 20080 citations

Real-space renormalization-group approach to the random transverse-field Ising model in finite dimensions

Ryoji Miyazaki, Hidetoshi Nishimori

The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent $\ensuremath{\nu}$ in one dimension and some previous results in the case of random ferromagnetic interactions are reproduced in two and three dimensions. We apply the scheme to spin glasses in transverse fields in two and three dimensions, which have not been analyzed very extensively. The phase diagrams and the critical exponent $\ensuremath{\nu}$ are obtained and evidence for the existence of an infinite-randomness fixed point in these models is found.The transverse-field Ising models with random exchange interactions in finite dimensions are investigated by means of a real-space renormalization-group method. The scheme yields the exact values of the critical point and critical exponent $\ensuremath{\nu}$ in one dimension and some previous results in the case of random ferromagnetic interactions are reproduced in two and three dimensions. We apply the scheme to spin glasses in transverse fields in two and three dimensions, which have not been analyzed very extensively. The phase diagrams and the critical exponent $\ensuremath{\nu}$ are obtained and evidence for the existence of an infinite-randomness fixed point in these models is found.

arXiv:1210.5053Physical Review EMar 25, 201324 citations

Spin-glass behavior from Migdal's recursion relations

Ciriyam Jayaprakash, J. Chalupa, Michael Wortis

The Edwards-Anderson model of a spin glass is studied by position-space renormalization-group techniques, using an inhomogeneous generalization of Migdal's approximate recursion relation. We treat the spin-1/2 Ising model with independently random nearest-neighbor interactions in dimensionalities $d=2, 3, \mathrm{and} 4$ . The phase diagram, which is in qualitative agreement with mean-field results, exhibits paramagnetic, ferromagnetic, antiferromagnetic, and spin-glass phases. The spin-glass and paramagnetic phases meet along an extended second-order phase boundary, which terminates in two tricritical points. Critical and tricritical exponents are calculated. The spin-glass specific-heat exponent turns out to be large and negative, compatibly with recent experiments which show a rounded specific-heat anomaly.The Edwards-Anderson model of a spin glass is studied by position-space renormalization-group techniques, using an inhomogeneous generalization of Migdal's approximate recursion relation. We treat the spin-1/2 Ising model with independently random nearest-neighbor interactions in dimensionalities $d=2, 3, \mathrm{and} 4$. The phase diagram, which is in qualitative agreement with mean-field results, exhibits paramagnetic, ferromagnetic, antiferromagnetic, and spin-glass phases. The spin-glass and paramagnetic phases meet along an extended second-order phase boundary, which terminates in two tricritical points. Critical and tricritical exponents are calculated. The spin-glass specific-heat exponent turns out to be large and negative, compatibly with recent experiments which show a rounded specific-heat anomaly.

Physical review. B, Solid stateFeb 1, 197784 citations

Monte Carlo study on phase transition of Ising spin glasses

Koji Fukushima

Jan 1, 19960 citations

An Ising model including field randomness and $\ifmmode\pm\else\textpm\fi{}J$ bond randomness is studied by renormalization-group theory in spatial dimensions

d=2

and 3. In

d=3,

with field randomness but no $\ifmmode\pm\else\textpm\fi{}J$ randomness, ferromagnetic and paramagnetic phases occur with no intervening spin-glass phase. Also in

d=3,

at sufficient $\ifmmode\pm\else\textpm\fi{}J$ randomness, a spin-glass phase occurs, but is replaced by the paramagnetic phase for any nonzero random field, also implying its disappearance for any nonzero uniform field. In

d=2,

no ferromagnetic phase under random fields and no spin-glass phase occur. Global phase diagrams uniting the random-field and spin-glass problems are evaluated. The strong violation of critical phenomena universality, previously found adjoining random-bond tricriticality in

d=3,

is seen here in

d=2.

d=2, 3, \mathrm{and} 4

. The phase diagram, which is in qualitative agreement with mean-field results, exhibits paramagnetic, ferromagnetic, antiferromagnetic, and spin-glass phases. The spin-glass and paramagnetic phases meet along an extended second-order phase boundary, which terminates in two tricritical points. Critical and tricritical exponents are calculated. The spin-glass specific-heat exponent turns out to be large and negative, compatibly with recent experiments which show a rounded specific-heat anomaly.