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Strong Coupling in Conserved Surface Roughening: A New Universality Class?
Fernando Caballero1, Cesare Nardini2, Frédéric van Wijland3
1DAMTP, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, United Kingdom.
Physical Review Letters
|August 8, 2018
Summary
The conserved Kardar-Parisi-Zhang (CKPZ) equation may be incomplete. A new term suggests a phase transition to a novel growth phase with non-mean-field behavior in dimensions greater than one.
Area of Science:
- Surface growth dynamics
- Nonlinear physics
- Statistical mechanics
Background:
- The Kardar-Parisi-Zhang (KPZ) equation governs nonlinear surface growth and roughening.
- The conserved KPZ (CKPZ) equation is proposed for specific conditions, exhibiting non-mean-field behavior only in dimensions d<2.
Purpose of the Study:
- To identify potential incompleteness in the CKPZ equation.
- To investigate the impact of a symmetry-allowed nonlinear gradient term on CKPZ behavior.
- To explore new universality classes in surface growth dynamics.
Main Methods:
- Renormalization group analysis at one-loop level.
- Theoretical modification of the CKPZ equation.
- Numerical integration of the modified model in d=2.
Main Results:
- The CKPZ equation was found to be incomplete, omitting a crucial nonlinear gradient term.
- A parameter regime was identified where the renormalization group flow diverges, indicating a phase transition.
- Numerical simulations in d=2 provided evidence for non-mean-field behavior in the new growth phase.
Conclusions:
- The modified CKPZ equation suggests a new universality class for surface growth, potentially governed by a strong-coupling fixed point.
- This new phase exhibits non-mean-field behavior for any spatial dimension d>1.
- The findings challenge existing universality class assumptions for conserved surface growth models.
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