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Critical Study of Hierarchical Lattice Renormalization Group in Magnetic Ordered and Quenched Disordered Systems: Ising and Blume–Emery–Griffiths Models

Fabrizio Antenucci, A. Crisanti, Luca Leuzzi

arXiv:1303.3829Journal of Statistical PhysicsMar 27, 201419 citations

Study of two dimensional anisotropic Ising models via a renormalization group approach

Farid Taherkhani, Hamed Akbarzadeh, Hadi Abroshan +3 more

Physica A Statistical Mechanics and its ApplicationsJul 30, 20133 citations

Phase diagrams and crossover in spatially anisotropic d=3 Ising, XY magnetic, and percolation systems: Exact renormalization-group solutions of hierarchical models

Aykut Erbaş, Aslı Tuncer, Burcu Yücesoy +1 more

Hierarchical lattices that constitute spatially anisotropic systems are introduced. These lattices provide exact solutions for hierarchical models and, simultaneously, approximate solutions for uniaxially or fully anisotropic d = 3 physical models. The global phase diagrams, with d = 2 and d = 1 to d = 3 crossovers, are obtained for Ising and XY magnetic models and percolation systems, including crossovers from algebraic order to true long-range order.

arXiv:cond-mat/0506716Physical Review EAug 24, 200520 citations

Lower critical dimension of the random-field XY model and the zero-temperature critical line

Kutay Akın, A. Nihat Berker

The random-field XY model is studied in spatial dimensions d=3 and 4, and in between, as the limit q→∞ of the q-state clock models, by the exact renormalization-group solution of the hierarchical lattice or, equivalently, the Migdal-Kadanoff approximation to the hypercubic lattices. The lower critical dimension is determined between 3.81<d_{c}<4. When the random field is scaled with q, a line segment of zero-temperature criticality is found in d=3. When the random field is scaled with q^{2}, a universal phase diagram is found at intermediate temperatures in d=3.The random-field XY model is studied in spatial dimensions d=3 and 4, and in between, as the limit q→∞ of the q-state clock models, by the exact renormalization-group solution of the hierarchical lattice or, equivalently, the Migdal-Kadanoff approximation to the hypercubic lattices. The lower critical dimension is determined between 3.81<d_{c}<4. When the random field is scaled with q, a line segment of zero-temperature criticality is found in d=3. When the random field is scaled with q^{2}, a universal phase diagram is found at intermediate temperatures in d=3.

arXiv:2203.11153Physical review. EJul 29, 202211 citations

Phenomenological renormalization group approach to the anisotropic two-layer Ising model

Behrouz Mirza, Kamran Mardani

arXiv:cond-mat/0402236The European Physical Journal BAug 1, 200316 citations

Renormalization Group Solution of the One-Dimensional Ising Model with a magnetic Field

Wei-Tou Ni

Chinese Journal of PhysicsJun 1, 19760 citations

Spatially Anisotropic d=3 Ising, XY Magnetic and Percolation Systems: Exact Renormalization-Group Solutions of Hierarchical Models

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Spatially Anisotropic d=3 Ising, XY Magnetic and Percolation Systems: Exact Renormalization-Group Solutions of Hierarchical Models

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