Regensburg 2025 – wissenschaftliches Programm

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TT: Fachverband Tiefe Temperaturen

TT 37: Correlated Electrons: Poster

TT 37.56: Poster

Mittwoch, 19. März 2025, 15:00–18:00, P4

Ising model on a sphere — •Grigorios Makris¹, Fabian Hassler², Stefan Wessel¹, and Ion Cosma Fulga^3,4 — ¹Institute for Theoretical Solid State Physics, RWTH Aachen University, Germany — ²Institute for Quantum Information, RWTH Aachen University, Germany — ³Institute for Theoretical Solid State Physics, IFW Dresden, Germany — ⁴Würzburg-Dresden Cluster of Excellence ct.qmat, Dresden, Germany

The study of the Ising models is of primary interest in the theory of phase transitions. The models have been extensively studied in flat space and analytical solutions exist in two dimensions. Their scaling behavior is known to substantial precision and confirms the theory of finite-size scaling.

Here, we study Ising models on the surface of a sphere. As it is generally not possible to place a regular lattice on a sphere, for arbitrary number of points, we implement the Fibonacci lattice. The lattice is tested to have a reasonably uniform distribution of points. In order to establish the expected SO(3) symmetry, we first solve the free-particle problem as a tight-binding model and then utilize the hopping coefficients as interaction terms on the Ising model. This is shown to yield better, approximate, SO(3) degeneracies on the low energy levels of the transverse-field Ising model. Having set up the Hamiltonian, we further investigate the critical point of the expected phase transition.

Keywords: Ising; transverse-field; Fibonacci; sphere