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title: ising model -- author: tim tejsner -- desc: visualization of the ising model -- script: lua -- input: gamepad or keyboard t=0 X = 28 Y = 15 J = 1 -- initial exchange interaction T = 25 -- initial temperature -- initialise matrix function BOOT() spins = {} for x=1,X do local row = {} for y=1,Y do if math.random(2) == 1 then table.insert(row, 1) else table.insert(row, -1) end end table.insert(spins, row) end end function draw_spins() for x=1,X do for y=1,Y do if spins[x][y] == 1 then spr(257,x*8,y*8,5) -- spin up else spr(258,x*8,y*8,5) -- spin down end end end end function get_total_energy() local E = 0 for x=1,X do for y=1,Y do E = E + get_energy_at_site(x, y) end end return E end function get_energy_at_site(x, y) local E = 0 -- get neighbours local up = {x=x,y=y-1} local down = {x=x,y=y+1} local left = {x=x-1,y=y} local right = {x=x+1,y=y} -- Apply PBC if y == 1 then up.y = Y end if y == Y then down.y = 1 end if x == 1 then left.x = X end if x == X then right.x = 1 end -- calculate energy E = E - J*spins[up.x][up.y]*spins[x][y] E = E - J*spins[down.x][down.y]*spins[x][y] E = E - J*spins[left.x][right.y]*spins[x][y] E = E - J*spins[right.x][right.y]*spins[x][y] return E end function metropolis_step() -- calculate energy local E = get_total_energy() -- flip random spin local x = math.random(1, X) local y = math.random(1, Y) spins[x][y] = spins[x][y]*(-1) -- calculate energy difference local dE = get_total_energy() - E -- generate random number local rand = math.random() if rand > 0.3*math.exp(-dE/T) then spins[x][y] = spins[x][y]*(-1) end end function TIC() for _=1, 10 do metropolis_step() end cls(5) draw_spins() local energy = get_total_energy() local e_str = string.format("E=%d", get_total_energy()) local t_str = string.format("T=%d", T) local j_str = string.format("J=%d", J) print(e_str,1,1,0) print(t_str,100,1,0) print(j_str,200,1,0) if btnp(0,60,6) then T = T+1 end if btnp(1,60,6) then T = T-1 end if T < 1 then T = 1 end if btnp(4,60,6) then J = -1*J end t = t+1 end