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Updated: Apr 7, 2026

Synthesis of Cyclic Polymers and Characterization of Their Diffusive Motion in the Melt State at the Single Molecule Level
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Topology-driven phase transitions in the classical monomer-dimer-loop model.

Sazi Li1, Wei Li1,2, Ziyu Chen1,3

  • 1Department of Physics, Beihang University, Beijing 100191, China.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|July 15, 2015
PubMed
Summary
This summary is machine-generated.

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This study explores monomer-dimer-loop models on a square lattice, revealing a second-order phase transition undetectable by local order parameters. A novel nonlocal string order parameter identifies topological ergodicity breaking in the loop-condensation phase.

Area of Science:

  • Statistical Mechanics
  • Condensed Matter Physics
  • Tensor Network Methods

Background:

  • Classical loop models are fundamental in statistical mechanics.
  • Doping these models with monomers and dimers introduces complex behaviors.
  • Understanding phase transitions in such systems is crucial for theoretical advancements.

Purpose of the Study:

  • Investigate classical loop models doped with monomers and dimers on a square lattice.
  • Analyze the thermodynamic properties and phase transitions using tensor network techniques.
  • Identify novel order parameters for topological phase transitions.

Main Methods:

  • Representing the partition function as a tensor network (TN).
  • Employing boundary matrix product state (MPS) techniques to contract the TN in the thermodynamic limit.

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  • Analyzing the transfer-matrix spectrum and developing nonlocal order parameters.

    • Main Results:

    • A second-order phase transition was identified between monomer-condensation and loop-condensation (LC) phases.
    • The transition is not detectable by local order parameters but exhibits distinct topological properties.
    • The LC phase shows two degenerate dominating eigenvalues and a nonvanishing nonlocal string order parameter.

    Conclusions:

    • The nonlocal string order parameter effectively identifies topological ergodicity breaking in the LC phase.
    • This parameter serves as a robust order parameter for detecting the discovered phase transitions.
    • The study advances the understanding of topological phases in doped loop models.