A model describing the relaxation dynamics of an interface of Ising-like systems is introduced. By means of renormalized field theory in $d=1+\ensuremath{\epsilon}$ dimensions the dynamic critical exponent is found as $z=2+\ensuremath{\epsilon}\ensuremath{-}\frac{1}{2}{\ensuremath{\epsilon}}^{2}+O({\ensuremath{\epsilon}}^{3})$. Interpolation with the known result near four dimensions yields good agreement with a high-temperature expansion and with recent real-space and Monte Carlo renormalization-group calculations in two dimensions.A model describing the relaxation dynamics of an interface of Ising-like systems is introduced. By means of renormalized field theory in $d=1+\ensuremath{\epsilon}$ dimensions the dynamic critical exponent is found as $z=2+\ensuremath{\epsilon}\ensuremath{-}\frac{1}{2}{\ensuremath{\epsilon}}^{2}+O({\ensuremath{\epsilon}}^{3})$. Interpolation with the known result near four dimensions yields good agreement with a high-temperature expansion and with recent real-space and Monte Carlo renormalization-group calculations in two dimensions.

Physical Review LettersDec 21, 1981134 citations

CRITICAL PHENOMENA NEAR TWO DIMENSIONS

WORLD SCIENTIFIC eBooksApr 1, 19930 citations

Dynamics and conductivity near quantum criticality

Snir Gazit, Daniel K. Podolsky, Assa Auerbach +1 more

Relativistic O( $N$ ) field theories are studied near the quantum-critical point in two space dimensions. We compute dynamical correlations by large-scale Monte Carlo simulations and numerical analytic continuation. In the ordered side, the scalar spectral function exhibits a universal peak at the Higgs mass. For $N=3$ and 4, we confirm its ${\ensuremath{\omega}}^{3}$ rise at low frequency. On the disordered side, the spectral function exhibits a sharp gap. For $N=2$ , the dynamical conductivity rises above a threshold at the Higgs mass (density gap), in the superfluid (Mott insulator) phase. For charged bosons (Josephson arrays), the power-law rise above the Higgs mass increases from two to four. Approximate charge-vortex duality is reflected in the ratio of imaginary conductivities on either side of the transition. We determine the critical conductivity to be ${\ensuremath{\sigma}}_{\mathrm{c}}^{*}=0.3(\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}4{e}^{2}/h$ and describe a generalization of the worm algorithm to $N>2$ . We use a singular value decomposition error analysis for the numerical analytic continuation.Relativistic O($N$) field theories are studied near the quantum-critical point in two space dimensions. We compute dynamical correlations by large-scale Monte Carlo simulations and numerical analytic continuation. In the ordered side, the scalar spectral function exhibits a universal peak at the Higgs mass. For $N=3$ and 4, we confirm its ${\ensuremath{\omega}}^{3}$ rise at low frequency. On the disordered side, the spectral function exhibits a sharp gap. For $N=2$, the dynamical conductivity rises above a threshold at the Higgs mass (density gap), in the superfluid (Mott insulator) phase. For charged bosons (Josephson arrays), the power-law rise above the Higgs mass increases from two to four. Approximate charge-vortex duality is reflected in the ratio of imaginary conductivities on either side of the transition. We determine the critical conductivity to be ${\ensuremath{\sigma}}_{\mathrm{c}}^{*}=0.3(\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}4{e}^{2}/h$ and describe a generalization of the worm algorithm to $N>2$. We use a singular value decomposition error analysis for the numerical analytic continuation.

arXiv:1309.1765Physical Review BDec 6, 201361 citations

CRITICAL PHENOMENA NEAR TWO DIMENSIONS

WORLD SCIENTIFIC eBooksJun 1, 20050 citations

Relativistic O(

N

) field theories are studied near the quantum-critical point in two space dimensions. We compute dynamical correlations by large-scale Monte Carlo simulations and numerical analytic continuation. In the ordered side, the scalar spectral function exhibits a universal peak at the Higgs mass. For

N=3

and 4, we confirm its ${\ensuremath{\omega}}^{3}$ rise at low frequency. On the disordered side, the spectral function exhibits a sharp gap. For

N=2

, the dynamical conductivity rises above a threshold at the Higgs mass (density gap), in the superfluid (Mott insulator) phase. For charged bosons (Josephson arrays), the power-law rise above the Higgs mass increases from two to four. Approximate charge-vortex duality is reflected in the ratio of imaginary conductivities on either side of the transition. We determine the critical conductivity to be ${\ensuremath{\sigma}}_{\mathrm{c}}^{*}=0.3(\ifmmode\pm\else\textpm\fi{}0.1)\ifmmode\times\else\texttimes\fi{}4{e}^{2}/h$ and describe a generalization of the worm algorithm to

N>2

. We use a singular value decomposition error analysis for the numerical analytic continuation.