We present a new cluster-update Monte Carlo algorithm for a fluctuating interface in the 3D Ising model. Critical slowing down is drastically reduced and the dynamical critical exponent at the roughening temperature of the 3D Ising model is found to be ${\mathit{z}}_{\mathrm{cl}}$ =0.44\ifmmode\pm\else\textpm\fi{}0.03. For the Metropolis algorithm we obtain ${\mathit{z}}_{\mathrm{Met}}$ =2.0\ifmmode\pm\else\textpm\fi{}0.1 while the Swendsen-Wang algorithm performs even worse than local updating. A new method which suppresses fluctuations in the two bulk phases is introduced to determine moments of the interfacial thickness.We present a new cluster-update Monte Carlo algorithm for a fluctuating interface in the 3D Ising model. Critical slowing down is drastically reduced and the dynamical critical exponent at the roughening temperature of the 3D Ising model is found to be ${\mathit{z}}_{\mathrm{cl}}$=0.44\ifmmode\pm\else\textpm\fi{}0.03. For the Metropolis algorithm we obtain ${\mathit{z}}_{\mathrm{Met}}$=2.0\ifmmode\pm\else\textpm\fi{}0.1 while the Swendsen-Wang algorithm performs even worse than local updating. A new method which suppresses fluctuations in the two bulk phases is introduced to determine moments of the interfacial thickness.

Physical Review LettersFeb 4, 199136 citations

Toward a 3d Ising model with a weakly-coupled string theory dual

Nabil Iqbal, John McGreevy

It has long been expected that the 3d Ising model can be thought of as a string theory, where one interprets the domain walls that separate up spins from down spins as two-dimensional string worldsheets. The usual Ising Hamiltonian measures the area of these domain walls. This theory has string coupling of unit magnitude. We add new local terms to the Ising Hamiltonian that further weight each spin configuration by a factor depending on the genus of the corresponding domain wall, resulting in a new 3d Ising model that has a tunable bare string coupling g_s g s . We use a combination of analytical and numerical methods to analyze the phase structure of this model as g_s g s is varied. We study statistical properties of the topology of worldsheets and discuss the prospects of using this new deformation at weak string coupling to find a worldsheet description of the 3d Ising transition.It has long been expected that the 3d Ising model can be thought of as a string theory, where one interprets the domain walls that separate up spins from down spins as two-dimensional string worldsheets. The usual Ising Hamiltonian measures the area of these domain walls. This theory has string coupling of unit magnitude. We add new local terms to the Ising Hamiltonian that further weight each spin configuration by a factor depending on the genus of the corresponding domain wall, resulting in a new 3d Ising model that has a tunable bare string coupling g_s g s . We use a combination of analytical and numerical methods to analyze the phase structure of this model as g_s g s is varied. We study statistical properties of the topology of worldsheets and discuss the prospects of using this new deformation at weak string coupling to find a worldsheet description of the 3d Ising transition.

arXiv:2003.04349SciPost PhysicsAug 13, 202027 citations

{\mathit{z}}_{\mathrm{cl}}

=0.44\ifmmode\pm\else\textpm\fi{}0.03. For the Metropolis algorithm we obtain

{\mathit{z}}_{\mathrm{Met}}

=2.0\ifmmode\pm\else\textpm\fi{}0.1 while the Swendsen-Wang algorithm performs even worse than local updating. A new method which suppresses fluctuations in the two bulk phases is introduced to determine moments of the interfacial thickness.