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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
+
+