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Related Experiment Video

Updated: Dec 14, 2025

Finite Element Modelling of a Cellular Electric Microenvironment

Finite Element Modelling of a Cellular Electric Microenvironment

Published on: May 18, 2021

Three-dimensional monopole-free CP^{N-1} models.

Andrea Pelissetto¹, Ettore Vicari²

¹Dipartimento di Fisica dell'Università di Roma Sapienza and Istituto Nazionale di Fisica Nucleare, Sezione di Roma I, I-00185 Roma, Italy.

Physical Review. E

|July 22, 2020

Summary

This study explores phase transitions in monopole-free CP^{N-1} models using Monte Carlo simulations. Results indicate continuous transitions for large N, differing from monopole-present models.

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Area of Science:

High-energy physics
Condensed matter physics
Quantum field theory

Background:

Investigating three-dimensional monopole-free CP^{N-1} models with U(N) global and U(1) gauge symmetries.
Understanding the impact of monopole absence on phase transition characteristics.

Purpose of the Study:

To determine the phase diagram and nature of phase transitions in these models.
To analyze the behavior for various N values (2, 4, 10, 15, 25) using numerical simulations.

Main Methods:

Monte Carlo simulations were employed for numerical analysis.
Focus on finite-temperature transitions and order parameter condensation.
Comparison with existing literature and field-theory predictions.

Main Results:

Finite-temperature transitions observed for all N.
N=2 results are inconclusive, possibly weak first-order or continuous with large corrections.
N=4, 10, 15 show weaker first-order transitions; N=25 suggests a conventional continuous transition.
Exclusion of the O(3) vector universality class for N=2.

Conclusions:

Monopole-free models exhibit continuous transitions for large N (including N=∞).
Results align with analytic large-N calculations for the N-component Abelian-Higgs model.
Phase transition nature is sensitive to monopole presence and N value.