Related Experiment Video
Updated: May 18, 2026
05:39
Scalable Quantum Integrated Circuits on Superconducting Two-Dimensional Electron Gas Platform
Published on: August 2, 2019
Stripe-tetragonal phase transition in the two-dimensional Ising model with dipole interactions: partition function
Jacyana S M Fonseca1, Leandro G Rizzi, Nelson A Alves
1Departamento de Física, FFCLRP, Universidade de São Paulo, Avenida Bandeirantes, 3900 Ribeirão Preto 14040-901, SP, Brazil. jacyanasaraiva@usp.br
Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|September 26, 2012
Summary
This study investigates the two-dimensional Ising model with dipole interactions, finding a single second-order phase transition. Our multicanonical simulations exclude a tricritical point, clarifying critical behavior in striped phases.
Area of Science:
- Statistical mechanics
- Condensed matter physics
- Computational physics
Background:
- The two-dimensional Ising model with dipole interactions exhibits complex phase behavior.
- Previous studies reported controversial findings regarding tricritical points in striped phases (h=1).
Purpose of the Study:
- To clarify the critical behavior of the two-dimensional Ising model with dipole interactions.
- To resolve discrepancies concerning the existence of a tricritical point in the striped phase region.
Main Methods:
- Multicanonical simulations were employed to achieve high statistics.
- Analysis of complex partition function zeros was performed.
- Finite size scaling relations were applied to critical exponents.
Main Results:
- Critical exponents (ν) derived from partition function zeros are consistent with a single second-order phase transition.
- The existence of a tricritical point in the studied region (δ=0.85-1) was excluded.
- Specific heat and susceptibility analyses supported the findings.
Conclusions:
- The critical behavior in the striped phase of the 2D Ising model with dipole interactions is characterized by a single second-order phase transition.
- The previously claimed tricritical point is not present in this region of the phase diagram.
Related Concept Videos
02:46Crystal Field Theory - Tetrahedral and Square Planar Complexes
Tetrahedral Complexes
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
Crystal field theory (CFT) is applicable to molecules in geometries other than octahedral. In octahedral complexes, the lobes of the dx2−y2 and dz2 orbitals point directly at the ligands. For tetrahedral complexes, the d orbitals remain in place, but with only four ligands located between the axes. None of the orbitals points directly at the tetrahedral ligands. However, the dx2−y2 and dz2 orbitals (along the Cartesian axes) overlap with the ligands less than the dxy,...
02:39Phase Transitions: Melting and Freezing
Heating a crystalline solid increases the average energy of its atoms, molecules, or ions, and the solid gets hotter. At some point, the added energy becomes large enough to partially overcome the forces holding the molecules or ions of the solid in their fixed positions, and the solid begins the process of transitioning to the liquid state or melting. At this point, the temperature of the solid stops rising, despite the continual input of heat, and it remains constant until all of the solid is...
01:14Atomic Nuclei: Nuclear Spin State Population Distribution
Near absolute zero temperatures, in the presence of a magnetic field, the majority of nuclei prefer the lower energy spin-up state to the higher energy spin-down state. As temperatures increase, the energy from thermal collisions distributes the spins more equally between the two states. The Boltzmann distribution equation gives the ratio of the number of spins predicted in the spin −½ (N−) and spin +½ (N+) states.
01:21Phase Transitions
A phase transition is the process in which a substance changes from one state of matter to another, like from a solid to a liquid, liquid to gas, or vice versa, at a specific temperature and under given pressure conditions. This change is spontaneous and is affected by alterations in temperature and pressure. These parameters impact the strength of the forces between molecules (intermolecular forces) in the substance.During a phase transition, both the initial and final phases of the substance...
02:31Phase Transitions
Whether solid, liquid, or gas, a substance's state depends on the order and arrangement of its particles (atoms, molecules, or ions). Particles in the solid pack closely together, generally in a pattern. The particles vibrate about their fixed positions but do not move or squeeze past their neighbors. In liquids, although the particles are closely spaced, they are randomly arranged. The position of the particles are not fixed—that is, they are free to move past their neighbors to occupy...
02:42Valence Bond Theory
Coordination compounds and complexes exhibit different colors, geometries, and magnetic behavior, depending on the metal atom/ion and ligands from which they are composed. In an attempt to explain the bonding and structure of coordination complexes, Linus Pauling proposed the valence bond theory, or VBT, using the concepts of hybridization and the overlapping of the atomic orbitals. According to VBT, the central metal atom or ion (Lewis acid) hybridizes to provide empty orbitals of suitable...