Lower Critical Dimension of the Random-Field Xy Model and the Zero-Temperature Critical Line
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Date
2022
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Amer Physical Soc
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Abstract
The random-field XY model is studied in spatial dimensions d = 3 and 4, and in between, as the limit q -> infinity 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.
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Hierarchical Lattices, Phase-Transitions, Critical-Behavior, Spin Systems, Ising-Model, Renormalization, Hierarchical Lattices, Phase-Transitions, Critical-Behavior, Spin Systems, Ising-Model, Renormalization
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Physical Review E
Volume
106
Issue
1