Finite size induces crossover temperature in growing spin chains.

Area of Science:

• Statistical Mechanics
• Complex Systems

Background:

• Investigating quenched spin models with asymmetrical interactions is crucial for understanding complex magnetic phenomena.
• External fields significantly influence the behavior of magnetic systems.

Purpose of the Study:

• To introduce and analyze a novel one-dimensional quenched spin model with asymmetrical Ising interactions.
• To explore the relationship between temperature, external field, and mean magnetization in finite systems.
• To assess the model's applicability to real-world data, such as online discussions.

Main Methods:

• Numerical simulations were employed to study the spin model.
• Analytical calculations based on Markov chain theory were performed.
• The model's behavior was analyzed concerning system size and temperature variations.

Main Results:

• A non-monotonous dependence of mean magnetization on temperature was observed for systems with external field < exchange coupling constant J.
• The crossover temperature (Tc) for maximal magnetization decays with increasing system size, following an inverse Lambert W function relationship.
• The phenomenon arises from an interplay between thermal fluctuations and initial cluster formation.

Conclusions:

• The developed spin model captures complex behaviors relevant to statistical mechanics.
• The model demonstrates potential for qualitatively describing chronological online emotional discussions, with spins representing emotional valence.
• The findings highlight the importance of initial conditions and thermal fluctuations in finite quenched systems.