Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Lattice Centering and Coordination Number02:33

Lattice Centering and Coordination Number

The structure of a crystalline solid, whether a metal or not, is best described by considering its simplest repeating unit, which is referred to as its unit cell. The unit cell consists of lattice points that represent the locations of atoms or ions. The entire structure then consists of this unit cell repeating in three dimensions. The three different types of unit cells present in the cubic lattice are illustrated in Figure 1.
Types of Unit Cells
Imagine taking a large number of identical...
Crystal Field Theory - Tetrahedral and Square Planar Complexes02:46

Crystal 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,...
Valence Bond Theory02:42

Valence 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...
Structures of Solids02:22

Structures of Solids

Solids in which the atoms, ions, or molecules are arranged in a definite repeating pattern are known as crystalline solids. Metals and ionic compounds typically form ordered, crystalline solids. A crystalline solid has a precise melting temperature because each atom or molecule of the same type is held in place with the same forces or energy. Amorphous solids or non-crystalline solids (or, sometimes, glasses) which lack an ordered internal structure and are randomly arranged. Substances that...
VSEPR Theory and the Effect of Lone Pairs04:01

VSEPR Theory and the Effect of Lone Pairs

Effect of Lone Pairs of Electrons on Molecule Geometry
The Seven Crystal Systems: Overview01:24

The Seven Crystal Systems: Overview

Crystals with various point group symmetries belong to different crystal classes, which are synonymous terms. Despite being in the same class, crystals may have distinct shapes, like cubes and octahedra. There are 32 three-dimensional point groups, all of which are systematically divided into seven crystal systems.The basic cubic crystal system, exemplified by NaCl, features orthogonal vectors (α = β = �� = 90°) of equal lengths (a = b = c). When specific requirements are not imposed on the...

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Long-Range Resonances in Quasiperiodic Many-Body Localization.

Physical review letters·2026
Same author

Backbone three-point correlation function in the two-dimensional Potts model.

Physical review. E·2026
Same author

Phase Transitions and Remnants of Fractionalization at Finite Temperature in the Triangular Lattice Quantum Loop Model.

Physical review letters·2025
Same author

Interaction-Driven Instabilities in the Random-Field XXZ Chain.

Physical review letters·2024
Same author

Lattice Realization of Complex Conformal Field Theories: Two-Dimensional Potts Model with Q>4 States.

Physical review letters·2024
Same author

Heisenberg spin chain with random-sign couplings.

Proceedings of the National Academy of Sciences of the United States of America·2024

Related Experiment Video

Updated: Jul 18, 2026

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
09:32

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

Classical dimers with aligning interactions on the square lattice.

Fabien Alet1, Yacine Ikhlef, Jesper Lykke Jacobsen

  • 1Laboratoire de Physique Théorique, UMR CNRS 5152, Université Paul Sabatier, 31062 Toulouse, France. alet@irsamc.ups-tlse.fr

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|December 13, 2006
PubMed
Summary

We studied dimers on a square lattice, finding a crystal melts into a critical phase via a Kosterlitz-Thouless transition. Adding monomers creates a new critical line in the Ashkin-Teller universality class.

More Related Videos

Fabricating van der Waals Heterostructures with Precise Rotational Alignment
09:25

Fabricating van der Waals Heterostructures with Precise Rotational Alignment

Published on: July 5, 2019

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
13:56

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Related Experiment Videos

Last Updated: Jul 18, 2026

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules
09:32

Stable DNA Motifs, 1D and 2D Nanostructures Constructed from Small Circular DNA Molecules

Published on: April 12, 2019

Fabricating van der Waals Heterostructures with Precise Rotational Alignment
09:25

Fabricating van der Waals Heterostructures with Precise Rotational Alignment

Published on: July 5, 2019

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations
13:56

Probe Type II Band Alignment in One-Dimensional Van Der Waals Heterostructures Using First-Principles Calculations

Published on: October 12, 2019

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Phase Transitions

Background:

  • The study focuses on close-packed dimers on a square lattice, a system exhibiting complex phase behavior.
  • Nearest-neighbor dimer interactions favor parallel alignment, leading to a crystalline phase at low temperatures.

Purpose of the Study:

  • To investigate the phase transitions and critical phenomena in a dimer model with nearest-neighbor interactions.
  • To analyze the effect of introducing monomers on the system's critical behavior.
  • To provide a theoretical interpretation using a Coulomb gas mapping and explore analytic results for noninteracting dimers.

Main Methods:

  • Large-scale Monte Carlo simulations and transfer matrix calculations were employed.
  • The system was mapped to a Coulomb gas model for theoretical interpretation.
  • Numerical calculations determined coupling constants and exponents with high precision.
  • Analytic methods including Bethe ansatz and free field analysis were used for the noninteracting case.

Main Results:

  • A Kosterlitz-Thouless phase transition was identified, melting the crystal into a high-temperature critical phase with continuously varying exponents.
  • The introduction of monomers led to a new critical line within the Ashkin-Teller universality class.
  • A tricritical point was found at finite temperature and monomer fugacity.
  • Analytic results for noninteracting dimer coverings were derived.

Conclusions:

  • The dimer model exhibits rich phase behavior driven by interactions and monomer introduction.
  • The Kosterlitz-Thouless transition and Ashkin-Teller universality class are key to understanding the system's critical properties.
  • The Coulomb gas mapping provides a powerful theoretical framework for analyzing such systems.