13 4-spin Ising Chain Simulation

13 : 4-spin Ising Chain Simulation


How it works

It runs the Metropolis-Hastings monte-carlo algorithm to simulate 4 Ising spins in a linear chain with two external neighbours and an external field. Every monte-carlo step (10 clock cycles) a random number is created through a 32-bit LFSR and is compared to an 8-bit representations of the acceptance probability of a random spin flip. Using the inputs for external neighbors, N of these circuits can be chained together to create a 4N spin Ising chain.

How to test

The design can be tested by enabling one of the neighbours (input 4 or 5) and leave all other inputs low, the system will evolve into a ground state with every other spin pointing up.


# Input Output
0 clock, clock input. segment a, Spin 0.
1 T0, LSB of the 3-bit temperature representation. segment b, Spin 1.
2 T1, Middle bit of the 3-bit temperature. segment c, Spin 2.
3 T2, MSB of the 3-bit temperature. segment d, Spin 3.
4 N1, Value of neighbour 1 (up/1 or down/0). segment e, Neighbour 2.
5 N2, Value of neighbour 2 (up/1 or down/0). segment f, Neighbour 1.
6 J, The sign of the NN coupling constant J. none
7 H, Value of the coupling to the external field H. segment h, MC Step Indicator.