Field Theory, Disorder and Simulations

J. J Alonso, M. A Muñoz

A study of the influence of different types of disorder on systems in the Ising universality class by employing both a dynamical field theory approach and extensive Monte Carlo simulations is presented. We reproduce some well-known results for the case of quenched disorder (random temperature and random field), and analyze the effect of four different types of time-dependent disorder scarcely studied so far in the literature. Some of them are of obvious experimental and theoretical relevance (as, for example, globally fluctuating temperatures or random fields). All the predictions coming from our field-theoretical analysis are fully confirmed by extensive simulations in two and three dimensions, and novel qualitatively different, non-Ising transitions are reported. Possible experimental setups designed to explore the described phenomenologies are also briefly discussed.

S. De Lillo, Pasquale Sodano, F. C. Khanna +1 more

Jincheng Zhang

This paper explores the potential of utilizing controlled disorder arrays to generate emergent quantum field theory patterns. We propose a novel system designed to create self-organizing quantum fields based on the precise arrangement of disorder, aiming for predictable and explanatory phenomena. The core mechanism involves a complex interplay of spatial and temporal disorder, leveraging mathematical modeling to predict and understand complex quantum behavior. The research focuses on establishing a framework for generating fundamental patterns within these arrays, offering a fundamentally different approach compared to current simulation methods. The system's potential implications for understanding and potentially manipulating quantum phenomena are significant.

Ben M. Gripaios

Giorgio Parisi A, Nicolas Sourlas

We show by numerical simulations that the correlation function of the random-field Ising model (RFIM) in the critical region in three dimensions has very strong fluctuations and that in a finite volume the correlation length is not self-averaging. This is due to the formation of a bound state in the underlying field theory. We argue that this nonperturbative phenomenon is not particular to the RFIM in 3D. It is generic for disordered systems in two dimensions and may also happen in other three-dimensional disordered systems.

James G. Glimm, Arthur M. Jaffe