Nucleation and growth in a 2D Ising Model with Monte Carlo Simulation

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SUMMARY

The discussion focuses on implementing umbrella sampling for a 2D Ising model using Monte Carlo simulations to analyze nucleation and growth phenomena. The user seeks clarification on whether to sample individual spins or predefined regions of spins and how to compute the energy associated with spin flips. Key concepts include analyzing nearest neighbors and understanding nucleation energy in the context of statistical mechanics. The conversation highlights the complexities of visualizing spin interactions and the need for foundational knowledge in statistical mechanics.

PREREQUISITES
  • Understanding of the 2D Ising model and its spin configurations
  • Familiarity with Monte Carlo simulation techniques
  • Knowledge of statistical mechanics principles, particularly nucleation
  • Proficiency in C programming for implementing simulations
NEXT STEPS
  • Research the implementation of umbrella sampling in Monte Carlo simulations
  • Learn about energy calculations in the Ising model, focusing on spin interactions
  • Study the concept of nucleation in statistical mechanics and its implications
  • Explore visualization techniques for spin configurations in lattice models
USEFUL FOR

This discussion is beneficial for physicists, computational scientists, and students working on statistical mechanics, particularly those interested in Monte Carlo methods and the Ising model.

kd215
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I'm currently working on a project for a code that does umbrella sampling of a 2-D Ising model [size LxL of a magnet (analyzing up or down spins)]. The next step is to take my code to analyze a nucleation region and its growth by varying the temperature above critical. Before I even attempt to write more c code, I thought I would ask on this forum to see if I'm interpreting this correctly: (I might sound really stupid with these interpretations, but I have a hard time visualizing this)

I sample the whole magnet and select spin i,j (some position in the lattice). Let's say it's an up spin, analyze its four (nearest) neighbors to see which others are up spins.

Or should I be looking for a region of all up (or down) spins of a predefined size (let's say a square of 3X3, so 9 adjacent spins in the same direction)?

Orrrr should I start with a lattice of entirely all one direction of spins?

And also, even from here I have a hard time understanding the idea of nucleation: so am I trying to compute the energy associated with flipping a down spin that is surrounded by a region of up spins? and the probability/energy associated with spins adjacent that spin also flipping to down?

I have a VERY difficult time understanding and interpreting the ideas of statistical mechanics and analyzing the Ising model so any basic explanations/help would be greatly appreciated!
Thanks-
 
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