Using a recently proposed new renormalization group method (tensor renormalization group), we analyze the Ising model on the two-dimensional square lattice. For the lowest-order approximation with two-domain wall states, it realizes the idea of coarse graining of domain walls. We write down explicit analytic renormalization transformation and prove that the picture of the coarse graining of the physical domain walls does hold for all physical renormalization group flows. We solve it to get the fixed point structure and obtain the critical exponents and the critical temperature. These results are very near to the exact values. We also briefly report the improvement using four-domain wall states.Using a recently proposed new renormalization group method (tensor renormalization group), we analyze the Ising model on the two-dimensional square lattice. For the lowest-order approximation with two-domain wall states, it realizes the idea of coarse graining of domain walls. We write down explicit analytic renormalization transformation and prove that the picture of the coarse graining of the physical domain walls does hold for all physical renormalization group flows. We solve it to get the fixed point structure and obtain the critical exponents and the critical temperature. These results are very near to the exact values. We also briefly report the improvement using four-domain wall states.

arXiv:1109.1377International Journal of Modern Physics BJul 20, 20095 citations

Renormalization Group on the Lattice

Andreas Wipf

Lecture notes in physicsJan 1, 20210 citations

Numerical renormalization group methods

Martin Andersson

Jan 1, 19990 citations

Numerical study of competing spin-glass and ferromagnetic order

Mikhail V. Simkin

Two- and three-dimensional random Ising models with a Gaussian distribution of couplings with variance J and nonvanishing mean value ${\mathrm{J}}_{0}$ are studied using the zero-temperature domain-wall renormalization group (DWRG). The DWRG trajectories in the ( ${\mathrm{J}}_{0}$ ,J) plane after rescaling can be collapsed on two curves: one for ${\mathrm{J}}_{0}$ /J> ${\mathrm{r}}_{\mathrm{c}}$ and the other for ${\mathrm{J}}_{0}$ /J ${\mathrm{r}}_{\mathrm{c}}$ . In the first case the DWRG flows are toward the ferromagnetic fixed point both in two and three dimensions while in the second case flows are towards a paramagnetic fixed point and spin-glass fixed point in two and three dimensions, respectively.Two- and three-dimensional random Ising models with a Gaussian distribution of couplings with variance J and nonvanishing mean value ${\mathrm{J}}_{0}$ are studied using the zero-temperature domain-wall renormalization group (DWRG). The DWRG trajectories in the (${\mathrm{J}}_{0}$,J) plane after rescaling can be collapsed on two curves: one for ${\mathrm{J}}_{0}$/J>${\mathrm{r}}_{\mathrm{c}}$ and the other for ${\mathrm{J}}_{0}$/J${\mathrm{r}}_{\mathrm{c}}$. In the first case the DWRG flows are toward the ferromagnetic fixed point both in two and three dimensions while in the second case flows are towards a paramagnetic fixed point and spin-glass fixed point in two and three dimensions, respectively.

arXiv:cond-mat/9609213Physical review. B, Condensed matterMay 1, 19973 citations

Renormalization Group Domain Walls from Phantom Symmetries

Jin Chen

We develop a systematic construction of renormalization group (RG) domain walls between two-dimensional rational conformal field theories. Using phantom currents, we consider an auxiliary chiral extension linked to the folded ultraviolet--infrared theory by a topological interface. The construction of RG walls then reduces to identifying suitable automorphism-twisted Cardy states in the auxiliary theory. We find two such types of automorphisms: outer automorphisms exchanging identical current algebra factors, as in Gaiotto's construction, and continuous inner automorphisms generated by the zero modes of spin-one phantom currents. In the latter case, the RG domain walls generically admit a continuous defect conformal manifold. We further show that, when an RG flow can be orbifolded to another one, the orbifold may lift defect conformal moduli of the RG brane constructed using inner automorphisms. The two types of RG branes can then be mapped to each other via a topological interface defined by the orbifold. We demonstrate the two types of RG brane construction via various examples of flows between non-unitary minimal models, from parafermions to minimal models, and between generalized parafermions. Many physical observables of the RG walls are computed non-perturbatively, including boundary entropies and spectra, and UV--IR operator mixings. We also find interesting nontrivial boundary monodromy: a closed cycle in the defect conformal moduli space can carry an RG domain wall into other distinct non-trivial conformal interfaces.We develop a systematic construction of renormalization group (RG) domain walls between two-dimensional rational conformal field theories. Using phantom currents, we consider an auxiliary chiral extension linked to the folded ultraviolet--infrared theory by a topological interface. The construction of RG walls then reduces to identifying suitable automorphism-twisted Cardy states in the auxiliary theory. We find two such types of automorphisms: outer automorphisms exchanging identical current algebra factors, as in Gaiotto's construction, and continuous inner automorphisms generated by the zero modes of spin-one phantom currents. In the latter case, the RG domain walls generically admit a continuous defect conformal manifold. We further show that, when an RG flow can be orbifolded to another one, the orbifold may lift defect conformal moduli of the RG brane constructed using inner automorphisms. The two types of RG branes can then be mapped to each other via a topological interface defined by the orbifold. We demonstrate the two types of RG brane construction via various examples of flows between non-unitary minimal models, from parafermions to minimal models, and between generalized parafermions. Many physical observables of the RG walls are computed non-perturbatively, including boundary entropies and spectra, and UV--IR operator mixings. We also find interesting nontrivial boundary monodromy: a closed cycle in the defect conformal moduli space can carry an RG domain wall into other distinct non-trivial conformal interfaces.

arXiv:2610.23529Oct 16, 20260 citations

Optimization and stabilization of functional renormalization group flows

Niklas Zorbach, Jonas Stoll, Jens Braun

Physical review. D/Physical review. D.Jan 1, 20250 citations

Two- and three-dimensional random Ising models with a Gaussian distribution of couplings with variance J and nonvanishing mean value

{\mathrm{J}}_{0}

are studied using the zero-temperature domain-wall renormalization group (DWRG). The DWRG trajectories in the (

{\mathrm{J}}_{0}

,J) plane after rescaling can be collapsed on two curves: one for

{\mathrm{J}}_{0}

/J>

{\mathrm{r}}_{\mathrm{c}}

and the other for

{\mathrm{J}}_{0}

{\mathrm{r}}_{\mathrm{c}}

. In the first case the DWRG flows are toward the ferromagnetic fixed point both in two and three dimensions while in the second case flows are towards a paramagnetic fixed point and spin-glass fixed point in two and three dimensions, respectively.