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Tensor Renormalization Group Meets Computer Assistance
Nikolay Ebel, Tom Kennedy, Slava Rychkov
Tensor renormalization group, originally devised as a numerical technique, is emerging as a rigorous analytical framework for studying lattice models in statistical physics. Here w…
Exact Diagonalization, Matrix Product States and Conformal Perturbation Theory Study of a 3D Ising Fuzzy Sphere Model
Andreas M. Läuchli, Loïc Herviou, Patrick H. Wilhelm +1
Numerical studies of phase transitions in statistical and quantum lattice models provide crucial insights into the corresponding Conformal Field Theories (CFTs). In higher dimensio…
Transfer Matrix and Lattice Dilatation Operator for High-Quality Fixed Points in Tensor Network Renormalization Group
Nikolay Ebel, Tom Kennedy, Slava Rychkov
Tensor network renormalization group maps study critical points of 2d lattice models like the Ising model by finding the fixed point of the RG map. In a prior work arXiv:2408.10312…
Rotations, Negative Eigenvalues, and Newton Method in Tensor Network Renormalization Group
Nikolay Ebel, Tom Kennedy, Slava Rychkov
In the tensor network approach to statistical physics, properties of the critical point of a 2D lattice model are encoded by a four-legged tensor which is a fixed point of an RG ma…
Four Lectures on the Random Field Ising Model, Parisi-Sourlas Supersymmetry, and Dimensional Reduction
Slava Rychkov
Numerical evidence suggests that the Random Field Ising Model loses Parisi-Sourlas SUSY and the dimensional reduction property somewhere between 4 and 5 dimensions, while a related…
The fate of Parisi-Sourlas supersymmetry in Random Field models
Apratim Kaviraj, Slava Rychkov, Emilio Trevisani
By the Parisi-Sourlas conjecture, the critical point of a theory with random field (RF) disorder is described by a supersymmeric (SUSY) conformal field theory (CFT), related to a $…