Optimizing ising for spin I>1/2

[zeta]

I am trying in vain to use simulated anneal to minimize an ising system with spin 7/2. This is a model for a pattern recognition task. The system is roughly 40^2 and the spin -7/2<I<7/2
ie., 2I+1 = 8 states per node. It's big.

The problem is that I can't work out what a thermal fluctuation corresponds to in this case or in other words how does one move between neighboring states? Take the TS problem, you simply rearrange coordinates. What's the analogous move here?
cheers

 

[zeta]

strictly speaking this is called the Heisenberg model, b/c I>1/2

 

[charng]

I understand your frustration in trying to optimize an Ising system with spin 7/2. This is a complex system, especially with a 40^2 size, and it can be challenging to determine the appropriate thermal fluctuation to move between neighboring states. In order to optimize this system, it may be helpful to first analyze the properties of the spin 7/2 system and its neighboring states. This will allow you to better understand the potential energy landscape of the system and determine the most efficient way to move between states.

One approach you could take is to use Monte Carlo simulations to explore the energy landscape and identify the most probable configurations of the system. This can help you determine the appropriate thermal fluctuations that will lead to the desired state.

Another approach is to consider using genetic algorithms, which have been successful in optimizing complex systems such as Ising models. These algorithms mimic natural selection and evolution to find the optimal solution for a given problem. By using a combination of these methods, you may be able to find a more efficient way to move between states and optimize your Ising system for spin 7/2.

It's also important to keep in mind that the Ising model is a simplified representation of a real-world system, and there may be limitations in its ability to accurately model complex systems. It may be beneficial to consider other models or approaches that may better suit your specific pattern recognition task.

In summary, optimizing an Ising system with spin 7/2 can be a challenging task, but by carefully analyzing the system and utilizing various methods such as Monte Carlo simulations and genetic algorithms, you may be able to find an efficient solution. It's important to keep an open mind and continue exploring different approaches to find the best solution for your specific problem.