A cluster Monte Carlo (MC) updating algorithm is presented for the antiferromagnetic $Z(q)$ model, into which Ising variables are embedded. Using MC simulations combined with the histogram technique, we were able to study the q-state clock model, for $q=5$ and $q=7,$ in $d=2$ and $d=3$ dimensions. The two-dimensional system exhibits a phase transition at temperature $T=0$ for both $q=5$ and $q=7$ system states. The critical exponents were derived as well as the ground state entropy for $T=0.$ Our results for the $q=5$ and the $q=7$ three-dimensional systems show that they exhibit a phase transition at nonzero temperature.A cluster Monte Carlo (MC) updating algorithm is presented for the antiferromagnetic $Z(q)$ model, into which Ising variables are embedded. Using MC simulations combined with the histogram technique, we were able to study the q-state clock model, for $q=5$ and $q=7,$ in $d=2$ and $d=3$ dimensions. The two-dimensional system exhibits a phase transition at temperature $T=0$ for both $q=5$ and $q=7$ system states. The critical exponents were derived as well as the ground state entropy for $T=0.$ Our results for the $q=5$ and the $q=7$ three-dimensional systems show that they exhibit a phase transition at nonzero temperature.

Physical review. B, Condensed matterMar 20, 20032 citations

Monte Carlo investigations of phase transitions: status and perspectives

Kurt Binder, Erik Luijten, Marcus Müller +2 more

arXiv:cond-mat/9908270Physica A Statistical Mechanics and its ApplicationsJun 1, 200032 citations

Histogram Monte Carlo renormalization group method for phase transition models without critical slowing down

Chin‐Kun Hu

Based on the subgraph expansions for phase transition models, we present a histogram Monte Carlo method to calculate the free energy and other physical quantities for such models as continuous functions of the system parameter. The method does not have any critical slowing down. We then use physical quantities thus obtained in a percolation renormalization group method to calculate critical point, critical exponents, and thermodynamic order parameter. Our method gives quite accurate results and may be applied to many phase transition models.Based on the subgraph expansions for phase transition models, we present a histogram Monte Carlo method to calculate the free energy and other physical quantities for such models as continuous functions of the system parameter. The method does not have any critical slowing down. We then use physical quantities thus obtained in a percolation renormalization group method to calculate critical point, critical exponents, and thermodynamic order parameter. Our method gives quite accurate results and may be applied to many phase transition models.

Physical Review LettersNov 9, 199248 citations

New multiple histogram method for studying phase transitions

Oliver Hammrich

The European Physical Journal BDec 1, 19939 citations

Reweighting histograms in quantum Monte Carlo studies of the Heisenberg model

Adauto J. F. de Souza, M. L. Lyra

In this communication, the histogram-reweighting technique is extended to quantum Monte Carlo studies of spin systems. The proposed method is applied to obtain equilibrium critical parameters of the quantum $S=1/2$ Heisenberg ferromagnet on simple cubic lattices. Our estimates are ${k}_{B}{T}_{c}/J=1.67764(2),$ ${U}^{*}=0.4504(1),$ $\ensuremath{\gamma}=1.397(20),$ $\ensuremath{\beta}=0.360(6),$ and $\ensuremath{\nu}=0.705(10)$, which are in perfect agreement with the best field-theory and high-temperature-series results. The method can readily be applied to general quantum-spin models, standing as an important tool for the study of quantum phase transitions.In this communication, the histogram-reweighting technique is extended to quantum Monte Carlo studies of spin systems. The proposed method is applied to obtain equilibrium critical parameters of the quantum $S=1/2$ Heisenberg ferromagnet on simple cubic lattices. Our estimates are ${k}_{B}{T}_{c}/J=1.67764(2),$ ${U}^{*}=0.4504(1),$ $\ensuremath{\gamma}=1.397(20),$ $\ensuremath{\beta}=0.360(6),$ and $\ensuremath{\nu}=0.705(10)$, which are in perfect agreement with the best field-theory and high-temperature-series results. The method can readily be applied to general quantum-spin models, standing as an important tool for the study of quantum phase transitions.

Physical review. B, Condensed matterMar 1, 200212 citations

A cluster Monte Carlo (MC) updating algorithm is presented for the antiferromagnetic

Z(q)

model, into which Ising variables are embedded. Using MC simulations combined with the histogram technique, we were able to study the q-state clock model, for

q=5

and

q=7,

d=2

and

d=3

dimensions. The two-dimensional system exhibits a phase transition at temperature

T=0

for both

q=5

and

q=7

system states. The critical exponents were derived as well as the ground state entropy for

T=0.

Our results for the

q=5

and the

q=7

three-dimensional systems show that they exhibit a phase transition at nonzero temperature.

S=1/2

Heisenberg ferromagnet on simple cubic lattices. Our estimates are

{k}_{B}{T}_{c}/J=1.67764(2),

{U}^{*}=0.4504(1),

$\ensuremath{\gamma}=1.397(20),$ $\ensuremath{\beta}=0.360(6),$ and $\ensuremath{\nu}=0.705(10)$, which are in perfect agreement with the best field-theory and high-temperature-series results. The method can readily be applied to general quantum-spin models, standing as an important tool for the study of quantum phase transitions.