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|
{-# LANGUAGE MultiParamTypeClasses #-}
import Control.Monad.Mersenne.Random
import Data.Char
import Data.Graph
import Data.Group
import Data.Monoid
import Data.Monoid.Action
import Data.Sequence
data Z2
= E0
| E1
deriving (Eq, Show)
data Ising
= Up
| Down
deriving (Eq, Show)
instance Semigroup Z2 where
E0 <> a = a
E1 <> a
| a == E0 = E1
| otherwise = E0
instance Monoid Z2 where
mempty = E0
mappend a b = a <> b
instance Group Z2 where
invert = id
instance Action Z2 Ising where
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
|
