a Dynamic Cluster Approximation for Second-Order Phase Transitions.

We explore the momentum-sector-selective metal-insulator transitions recently found in the eight-site dynamical cluster approximation to the two-dimensional Hubbard model. The phase diagram in the space of interaction and second-neighbor hopping is established. The initial transitions from Fermi-liquid-like to sector-selective phases are found to be of second order, caused by the continuous opening of an energy gap whereas the other transitions are found to be of first order. In the sector-selective phase the Fermi surface regions which are not gapped are found to have a non-Fermi-liquid self-energy. We demonstrate that the phenomenon is not caused by the Van Hove divergence in the density of states. The sector-selective and insulating phases are characterized by a cluster spin-correlation function that is strongly peaked at the commensurate antiferromagnetic wave vector $(\ensuremath{\pi},\ensuremath{\pi})$ but the model has no nematic instability. Comparison to dynamical mean-field studies on smaller clusters is made.We explore the momentum-sector-selective metal-insulator transitions recently found in the eight-site dynamical cluster approximation to the two-dimensional Hubbard model. The phase diagram in the space of interaction and second-neighbor hopping is established. The initial transitions from Fermi-liquid-like to sector-selective phases are found to be of second order, caused by the continuous opening of an energy gap whereas the other transitions are found to be of first order. In the sector-selective phase the Fermi surface regions which are not gapped are found to have a non-Fermi-liquid self-energy. We demonstrate that the phenomenon is not caused by the Van Hove divergence in the density of states. The sector-selective and insulating phases are characterized by a cluster spin-correlation function that is strongly peaked at the commensurate antiferromagnetic wave vector $(\ensuremath{\pi},\ensuremath{\pi})$ but the model has no nematic instability. Comparison to dynamical mean-field studies on smaller clusters is made.

arXiv:0909.1795Physical Review BDec 1, 2009112 citations

Nematic phase in the J1−J2 square-lattice Ising model in an external field

Alejandra I. Guerrero, Daniel A. Stariolo, Noé G. Almarza

The J(1)-J(2) Ising model in the square lattice in the presence of an external field is studied by two approaches: the cluster variation method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and disordered phases. Suitable order parameters are defined, and the phase diagram of the model is obtained. Monte Carlo simulations are in qualitative agreement with the CVM results, giving support to the presence of the new Ising-nematic phase. Phase diagrams in the temperature-external field plane are obtained for selected values of the parameter κ=J(2)/|J(1)| which measures the relative strength of the competing interactions. From the CVM in the square approximation we obtain a line of second order transitions between the disordered and nematic phases, while the nematic-stripes phase transitions are found to be of first order. The Monte Carlo results suggest a line of second order nematic-disordered phase transitions in agreement with the CVM results. Regarding the stripes-nematic transitions, the present Monte Carlo results are not precise enough to reach definite conclusions about the nature of the transitions.The J(1)-J(2) Ising model in the square lattice in the presence of an external field is studied by two approaches: the cluster variation method (CVM) and Monte Carlo simulations. The use of the CVM in the square approximation leads to the presence of a new equilibrium phase, not previously reported for this model: an Ising-nematic phase, which shows orientational order but not positional order, between the known stripes and disordered phases. Suitable order parameters are defined, and the phase diagram of the model is obtained. Monte Carlo simulations are in qualitative agreement with the CVM results, giving support to the presence of the new Ising-nematic phase. Phase diagrams in the temperature-external field plane are obtained for selected values of the parameter κ=J(2)/|J(1)| which measures the relative strength of the competing interactions. From the CVM in the square approximation we obtain a line of second order transitions between the disordered and nematic phases, while the nematic-stripes phase transitions are found to be of first order. The Monte Carlo results suggest a line of second order nematic-disordered phase transitions in agreement with the CVM results. Regarding the stripes-nematic transitions, the present Monte Carlo results are not precise enough to reach definite conclusions about the nature of the transitions.

arXiv:1501.04023Physical Review EMay 14, 201527 citations

On the scaling behaviour of second-order phase transitions

R. P. Van Royen

Lettere al nuovo cimento della societa italiana di fisica/Lettere al nuovo cimentoJan 1, 19761 citation

Dynamical cluster approximation study of electron localization in the extended Hubbard model

Hanna Terletska, Sergei Iskakov, Thomas Maier +1 more

We perform a detailed study of the phase transitions and mechanisms of electron localization in the extended Hubbard model using the dynamical cluster approximation on a $2\ifmmode\times\else\texttimes\fi{}2$ cluster. We explore the interplay of charge order and Mott physics. We find that a nearest-neighbor Coulomb interaction $V$ causes ``screening'' effects close to the Mott phase transition, pushing the phase boundary to larger values of $U$ . We also demonstrate the different effects of $V$ on correlations in metallic and insulating regimes, and document the different correlation aspects of charge order and Mott states.We perform a detailed study of the phase transitions and mechanisms of electron localization in the extended Hubbard model using the dynamical cluster approximation on a $2\ifmmode\times\else\texttimes\fi{}2$ cluster. We explore the interplay of charge order and Mott physics. We find that a nearest-neighbor Coulomb interaction $V$ causes ``screening'' effects close to the Mott phase transition, pushing the phase boundary to larger values of $U$. We also demonstrate the different effects of $V$ on correlations in metallic and insulating regimes, and document the different correlation aspects of charge order and Mott states.

arXiv:2105.09414Physical review. B./Physical review. BAug 16, 202122 citations

The Statistical Mechanics of Phase Transitions.

J. D. Gunton

Jan 1, 19670 citations

V

causes ``screening'' effects close to the Mott phase transition, pushing the phase boundary to larger values of

U

. We also demonstrate the different effects of

V

on correlations in metallic and insulating regimes, and document the different correlation aspects of charge order and Mott states.