Correlated noise and critical dimensions

Area of Science:

• Statistical Mechanics
• Condensed Matter Physics
• Non-equilibrium Systems

Background:

• The Mermin-Wagner theorem states that continuous symmetry breaking is impossible in dimensions d≤2 for equilibrium systems.
• This limitation is a fundamental concept in understanding phase transitions and critical phenomena.
• Non-equilibrium systems offer potential avenues to bypass established equilibrium constraints.

Purpose of the Study:

• To investigate the circumvention of the Mermin-Wagner theorem's limitation in non-equilibrium systems.
• To analyze the impact of spatiotemporally correlated and anticorrelated noise on critical dimensions.
• To explore phenomena like hyperuniformity and giant number fluctuations in driven systems.

Main Methods:

• Dimensional analysis was employed to compute critical dimensions for the O(n) model under correlated noise.
• The spherical model (large-n limit of O(n)) was analyzed to derive critical dimensions and exponents analytically.
• Investigated the behavior of the spherical model with correlated noise above the critical point.

Main Results:

• Spatiotemporally correlated noise increases critical dimensions, while anticorrelated noise decreases them.
• Analytical calculations for the spherical model confirm these trends and provide critical exponents.
• The spherical model with correlated noise exhibits hyperuniformity and giant number fluctuations even above criticality.

Conclusions:

• The Mermin-Wagner theorem's prohibition of continuous symmetry breaking can be overcome in non-equilibrium settings.
• The nature of noise correlation (positive or negative) critically influences the system's dimensionality and phase behavior.
• Driven systems can display unique emergent properties like hyperuniformity and giant number fluctuations.