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{-# LANGUAGE MultiParamTypeClasses #-}
import Data.Sequence
import Data.Monoid
import Data.Monoid.Action
import Data.Group
import Data.Char
import Data.Graph
import Control.Monad.Mersenne.Random
data Z2 = E0 | E1 deriving (Eq, Show)
data Ising = Up | Down deriving (Eq, Show)
instance Semigroup Z2 where
-- Z2 is a semigroup
E0 <> a = a
E1 <> a | a == E0 = E1
| otherwise = E0
instance Monoid Z2 where
-- Z2 is a monoid
mempty = E0
mappend a b = a <> b
instance Group Z2 where
-- Z2 is a group
invert = id
instance Action Z2 Ising where
-- Z2 has an action on Ising spins
act E0 a = a
act E1 a | a == Up = Down
| otherwise = Up
squareLatticeEdges d l = [(i, (l^j) * quot i (l^j) + mod (l^j + i + s * l^(j-1)) (l^j)) | j <- [1..d], i <- [0..(l^d)-1], s <- [-1, 1]]
ghostEdges n = [(n, i) | i <- [0..n-1]] ++ [(i, n) | i <- [0..n-1]]
squareLattice d l = buildG (0, l^d) ((squareLatticeEdges d l) ++ ghostEdges (l^d))
data State r x = State { ghost :: r, spins :: Seq x }
j :: Ising -> Ising -> Integer
j a b | a == b = 1
| otherwise = -1
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