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the problem of human segregation is an important problem of society and politics even in the 21st century @xcite .
social sciences have been investigating the reasons and and nature of segregation for a long time .
sociologist have introduced several models , one of them is the schelling model @xcite . from physicist point of view that model is a 3-state voter - type non - equilibrium model ( groups a , b and empty ) , with spin - exchange dynamics at zero temperature ( @xmath0 ) on a 2-dimensional square lattice .
although the model describes a segregation by a quench without external reasons , unwanted frozen states may also occur .
recently it was shown by computer simulations @xcite that there exists a simpler model , namely the glauber - ising model @xcite , which captures the essence of human segregation .
besides that , the usage of the simple @xmath1 spin - flip dynamics makes it computationally easier and one can avoid the frozen states of the schelling model . in this model
the temperature plays the role of a global tolerance ; by varying it , the model may or may not evolve into the ordered ( segregated ) state .
however a constant , global tolerance is rather artificial in a society , it can vary from individual to individual and can change in time as well . by introducing a local , time dependent temperature ( tolerance ) , with a feedback mechanism from the local neighborhood
the model becomes more realistic .
the results do not change too much @xcite , a self - organization of the average temperature occurs .
the parameters of this model are the global rate of forgetting ( of tolerance ) and the response of local tolerances on the neighborhood .
the sum of these local changes determine the local temperature .
hereafter this self - organized segregation model will be called so - seg model .    stepping further towards more realistic models
, one can pose the question what happens to this model if the decision of individuals are affected by an independent external noise as well .
the external noise can be an artifact of a random environment , housing , moving situation , presence of shopping centers ... etc .
the external noise introduced here as a second temperature , i.e. individuals are connected to a second heath bath .
two - temperature two - state voter - type models have been investigated intensively recently and have become the prototypes of non - equilibrium models ( for a review see @xcite ) .
an important finding of these studies was the discovery of relevant factors affecting the phase transitions of models exhibiting @xmath2 ( up - down ) symmetry @xcite .
in particular models with general , isotropic spin - flip dynamics maintaining the @xmath2 symmetry can be classified as two temperature models , where one temperature controls the bulk , the other the interface fluctuations .
the ising model is a special case of these models , where both temperatures are nonzero and the time - reversal symmetry drives the system into an equilibrium state . the transition of these @xmath2 symmetric , two - temperature models has been found to be continuous , ising type unless the bulk temperature is zero . in the latter case
it is first order , voter model class type @xcite . in this work
i investigate the effect of a second temperature applied as an external , independent heat - bath to the spins of the so - seg model .
the model is defined on 2-dimensional square lattice , with periodic boundary conditions and ising spins ( @xmath3 ) distributed initially randomly ( zero initial magnetization = no segregation ) .
the kinetics follows a glauber spin - flip ( sequential ) update with heath bath acceptance rate ( see ref .  ) , depending on the local temperatures . in the so - seg model
each individual has four interacting nearest neighbors and a randomized initial local temperature , with an average value @xmath4 .
this local temperature is lowered by @xmath5 at each update for modeling the loss of tolerance .
this alone would just make a quench to @xmath6 with domain coarsening .
to model people s awareness of the dangers of segregation they can increase their own temperature ( tolerance ) by @xmath7 , if all four neighbors of an individual belong to the same group as @xmath8 .
if all four neighbors belong to the different group the local temperature is decreased by the same amount .
our external noise is described by a heat bath of a second temperature @xmath9 applied to the decisions
. the actual spin - flip will be the logical or of internal and external flip decisions .
the magnetization @xmath10 , the average number of like neighbors minus unlike neighbors @xmath11 , and the average self - organizing internal temperature ( tolerance ) @xmath12 is followed up to @xmath13 monte carlo sweeps ( mcs ) of the lattice .
the simulations were performed on @xmath14 , @xmath15 and @xmath16 sized square lattices , up to @xmath13 mcs , with cooling rates : @xmath17 and tolerance steps : @xmath18 .
the phase transition of the so - seg model is at @xmath19 @xcite , so @xmath20 corresponds to super - critical , @xmath21 to sub - critical situations .
as figure ( [ fig0 ] ) shows the inclusion of a small second temperature @xmath22 does not change the composition of neighbors and @xmath23 in the steady state ( as @xmath24 ) .
the same can be seen by plotting @xmath25 ( see fig.([fign ] ) ) and the average internal temperature of individuals ( fig.([figt ] ) ) . for stronger external noise
the domains are destroyed , but the average tolerance goes to zero too .
this means that the unsegregated state can be maintained with the help of strong external noise , without worrying about people s local tolerance .
the same analysis for @xmath21 resulted in similar trends in @xmath26 ( see fig.[figninf ] ) and in the average tolerance @xmath27 .
note that one observe even a weak increase in the asymptotic values for @xmath28 .
running the simulations on larger sizes there were no change in this , excluding the possibility of finite size errors .    by increasing the second temperature @xmath9 the transitions of @xmath29 ( see fig.([figninf ] ) ) and
@xmath30 are very smeared .
the magnetization density @xmath31 on the other hand shows a sharp fall , indicating a first order phase transition at @xmath32 . a fitting attempt using the form @xmath33 did not result in agreement with the 2d ising class continuous phase transition behavior , characterized by @xmath34 @xcite .
furthermore a hysteresis cycle can also be found by starting the simulations with different initial conditions ( ordered vs. disordered ) , which is a clear hallmark of a first order phase transition .
this is in contrast with the results for two - temperature @xmath2 symmetric models exhibiting ising transition in 2d ( the bulk noise in nonzero of course ) .
one may understand the discontinuous transition here by realizing that this model is effectively a coupled system : ising + temperate field .
the temperatures can increase if at least four neighbors are in the same state and decrease without condition . in the language of reaction diffusion systems
it is a quadruple model , where at least for neighbors are needed for a creation but the removal is spontaneous .
it is well known that in 2d such a quadruple model exhibits a first order transition @xcite .
simulations with different initial temperatures ( @xmath35 ) , cooling rates ( @xmath36 ) and @xmath7 have not resulted in changes in the transition point @xmath37 .
a two - temperature , self - organized ising - schelling model has been introduced and investigated by numerical simulations . a low second temperature , which represents the external noise to the decision of individuals for moving does not change the segregation behavior of the model .
a temperature bigger than @xmath38 randomizes the segregated , ordered domains and results in low average tolerance of individuals .
while the self - organized tolerance and the average composition of the steady state show continuous variation on @xmath9 the magnetization exhibits a first order phase transition .
the threshold did not show considerable dependence on the model parameters .
the author thanks d. stauffer for motivating and discussing his study and providing the code of ref .
@xcite for simulations .
support from the hungarian research fund otka ( grant no .
t-046129 ) during this study is gratefully acknowledged .
a two - temperature ising - schelling model is introduced and studied for describing human segregation . the self - organized ising model with glauber kinetics simulated by mller et al . 
 exhibits a phase transition between segregated and mixed phases mimicking the change of tolerance ( local temperature ) of individuals . 
 the effect of external noise is considered here as a second temperature added to the decision of individuals who consider change of accommodation . a numerical evidence is presented for a discontinuous phase transition of the magnetization .