Spontaneous Gauged O(<italic style="font-style: italic">N</italic>) Symmetry Breaking in Polymer Crystallization

Mai Zhou; Gui-Qiu Ma; Zhe Ma

doi:10.1007/s10118-026-3590-0

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Spontaneous Gauged O(N) Symmetry Breaking in Polymer Crystallization

RESEARCH ARTICLE | Updated：2026-04-30

- Spontaneous Gauged O(N) Symmetry Breaking in Polymer Crystallization
- Chinese Journal of Polymer Science Vol. 44, Issue 5, Pages: 1540-1552(2026)
- Affiliations：
  
  School of Materials Science and Engineering, Tianjin University, Tianjin 300072, China
- Author bio：
  
  zhe.ma@tju.edu.cn
- Funds：
- DOI：10.1007/s10118-026-3590-0
  CLC：
- Received：04 December 2025，
  
  Revised：2026-01-15，
  
  Accepted：25 January 2026，
  
  Online First：16 April 2026，
  
  Published：05 May 2026
- Accepted：
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Zhou, M.; Ma, G. Q.; Ma, Z. Spontaneous gauged O(N) symmetry breaking in polymer crystallization. Chinese J. Polym. Sci. 2026, 44, 1540–1552

Mai Zhou, Gui-Qiu Ma, Zhe Ma. Spontaneous Gauged O(N) Symmetry Breaking in Polymer Crystallization[J]. Chinese Journal of Polymer Science, 2026, 44(5): 1540-1552.
Zhou, M.; Ma, G. Q.; Ma, Z. Spontaneous gauged O(N) symmetry breaking in polymer crystallization. Chinese J. Polym. Sci. 2026, 44, 1540–1552 DOI： 10.1007/s10118-026-3590-0.

Mai Zhou, Gui-Qiu Ma, Zhe Ma. Spontaneous Gauged O(N) Symmetry Breaking in Polymer Crystallization[J]. Chinese Journal of Polymer Science, 2026, 44(5): 1540-1552. DOI： 10.1007/s10118-026-3590-0.

摘要

The Self-Avoiding String in polymer melts corresponds to O(

) × U(1) symmetry. Crystallization (chemical potential) induces its breaking into

while entanglements act as gauge fields

shifting the ordering process from a second-order to a first-order phase transition.

Abstract

The long-range order and intrinsic entanglement of polymer play a crucial role in crystallization and the corresponding melting relaxation which

however

are rarely treated as a form of symmetry. In this work

a field model is developed based on a self-avoiding random string with open ends

where time dimension for string vibrations is added and the dynamics of chain vibrations is captured by a

$$ \phi^4 $$

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theory with O(

) symmetry. The long-range order triggered by crystallization is referred to the scalar's breaking in grand canonical ensemble

while entanglement is considered as a geometric dynamic effect in absence of closed loops

rather than chain topology. For the entanglement

there are interactions among the replica scalar's components

via

the gauged O(

) symmetry. The infrared stability at

$$ d = 3+1 $$

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requires

$$ N = 2 $$

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thus the gauge-scalar theory is reduced to Coleman-Weinberg model in the rest frame. The finite-temperature effect causes the second-order phase transition related to scalar's breaking to become first-order with a metastable region

depending on the gauge coupling

. These modeling results are helpful in understanding the crystallization and melting behavior of polymer

including the difference of the extrapolated temperatures in Gibbs-Thomson equation

and the re-entanglement and the vanishing of long-range order in melt relaxation.

关键词

Keywords

references

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⁰

Spontaneous Gauged O(N) Symmetry Breaking in Polymer Crystallization

DOI：10.1007/s10118-026-3590-0

摘要

Abstract

关键词

Keywords

references