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 Experiment Videos

Random trimer tilings.

Anandamohan Ghosh1, Deepak Dhar, Jesper L Jacobsen

  • 1Department of Theoretical Physics, Tata Institute of Fundamental Research, Homi Bhabha Road, Mumbai 400 005, India. ananda@theory.tifr.res.in

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|March 16, 2007
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

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

Sort by
Same author

Dual influence of transcriptional and translational kinetics on gene expression noise.

Physical review. E·2025
Same author

Asymmetric Simple Exclusion Process on the Percolation Cluster: Waiting Time Distribution in Side Branches.

Physical review letters·2025
Same author

Cusp singularities in the distribution of orientations of asymmetrically pivoted hard disks on a lattice.

Physical review. E·2023
Same author

Absence of Mobility Edge in Short-Range Uncorrelated Disordered Model: Coexistence of Localized and Extended States.

Physical review letters·2023
Same author

Phases of the hard-plate lattice gas on a three-dimensional cubic lattice.

Physical review. E·2023
Same author

Spontaneous layering and power-law order in the three-dimensional fully packed hard-plate lattice gas.

Physical review. E·2023
Same journal

Tension on dsDNA bound to ssDNA-RecA filaments may play an important role in driving efficient and accurate homology recognition and strand exchange.

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Amplitude-phase coupling drives chimera states in globally coupled laser networks [Phys. Rev. E 91, 040901(R) (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Shapes of sedimenting soft elastic capsules in a viscous fluid [Phys. Rev. E 92, 033003 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Erratum: Attenuation of excitation decay rate due to collective effect [Phys. Rev. E 90, 022142 (2014)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Role of connectivity and fluctuations in the nucleation of calcium waves in cardiac cells [Phys. Rev. E 92, 052715 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
Same journal

Publisher's Note: Lattice Boltzmann approach for complex nonequilibrium flows [Phys. Rev. E 92, 043308 (2015)].

Physical review. E, Statistical, nonlinear, and soft matter physics·2016
See all related articles

We study linear trimer tilings on a square lattice. Our research reveals exponential block growth and estimates entropy per site, suggesting conformal invariance in the continuum limit.

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Combinatorics

Background:

  • Tiling problems are fundamental in statistical mechanics and combinatorics.
  • Understanding the properties of lattice tilings provides insights into phase transitions and critical phenomena.

Purpose of the Study:

  • To analyze the statistical properties of square lattice tilings using linear trimers.
  • To investigate the thermodynamic limit and continuum behavior of these tilings.
  • To explore conformal invariance and scaling dimensions within the trimer tiling model.

Main Methods:

  • Constructing a conserved functional for cylinder tilings.
  • Block diagonalization of the transfer matrix.
  • Numerical diagonalization of large blocks.

Related Experiment Videos

  • Monte Carlo simulations of height variables.

    • Main Results:

    • The number of blocks grows exponentially with cylinder circumference (m).
    • The largest eigenvalue block dimension scales as (32/13)^m.
    • Estimated entropy per site in the thermodynamic limit: S_infinity = 0.158520 ± 0.000015.
    • Numerical evidence for conformal invariance in the continuum limit.
    • Logarithmic growth of height-height correlations and power-law decay of orientation-orientation correlations.

    Conclusions:

    • The study provides a detailed analysis of linear trimer tilings, bridging discrete and continuous models.
    • The findings support the presence of conformal invariance, a key characteristic of critical phenomena.
    • The model exhibits rich statistical behavior, including logarithmic and power-law correlations.