I assume that by "positive" you men an enhancement of SAR and by "negative" a reduction of SAR. Is that correct?

If different researchers have found opposite results then it may be that both are right and that the answer is not universal but may depend on details such as the geometrical arrangement of the particles.

To appreciate that it would matter to understand the mechanisms that lead to either an enhancement or a reductio of SAR due to dipolar interactions. In this respect I am not familiar enough with the mechanisms governing SAR to give an answer.

Yet, there are other cases of seemingly contradicting effects reported for interacting particles. Strong interactions can slow down thermal fluctuations ("collective blocking" or super spin glasses) but has also reported to enhance the fluctuations (see e.g. P.Allia et al in their work on Co particles in metallic (Ag?) matrices).

This is still an open question and the most straightforward answer is: it depends. In general, most authors report a decrease of the heating ability per unit mass of magnetic material when increasing concentration, such as in:

http://pubs.acs.org/doi/abs/10.1021/jp912076f

http://link.springer.com/article/10.1007%2Fs10765-010-0799-4

However, some special cases have been found in the last few years. It has been shown that chain formation improves the heating efficiency of the formed structures with respect to their well-dispersed counterparts: 

http://www.nature.com/srep/2013/131007/srep02887/full/srep02887.html

Highly agglomerated nanoflowers show also improved heating ability:

dx.doi.org/10.1021/jp3025478

Some experimental features make also difficult reach a unique conclussion: the heating ability of the samples are usually measured under different field parameters, making it sometimes clueless comparing data among authors, and a big incertainty is usually present in mass determination and heating ramp measurement. Most authors report their heating ability measurements in fluids, but it is still unclear whether or not the nanoparticles can form structures in presence of alternating magnetic fluids, so that even at very low concentrations the nanoparticles cannot be considered as not interacting. An accurate description of the spatial distribution of magnetic nanoparticles is usually missing in most reports.

And last but not least, the interactions can be expected to have an effect dependent on the anisotropy of the material, as can be seen in 

http://pubs.acs.org/doi/abs/10.1021/jp0464526

Dear Prof. Fauth

Thanks for you answer. your suggestion is correct. the heat generation in magnetic hyperthermia arise from two mechanism

1- Neel relaxation which related to superspins dynamics

2- Brownian relaxation which is due to rotation of nanoparticle itself inside a fluid.

In the case of aggregate nano particles and presence of complex interactions both mechanism affected by interactions strength. As Irene said above it is an open question that, if interactions increase or decrease the heat generation of magnetic nanoparticles in presence of a AC field. following references could be helpful but the results are not universal:

http://scitation.aip.org/content/aip/journal/jap/108/7/10.1063/1.3488881?ver=pdfcov

http://scitation.aip.org/content/aip/journal/apl/95/8/10.1063/1.3211120?ver=pdfcov

http://journals.aps.org/prb/abstract/10.1103/PhysRevB.87.174419

http://iopscience.iop.org/0022-3727/46/4/045002

Dear Irene Andreu,

Thanks for your useful comments. It seems that you are working in this field. and your suggested references were useful but as you mentioned the answer to this question is not clear yet although most of researchers reported a decreases in hyperthermia output by increasing interactions strength.

The controversy in this subject is quite logic and difficult to solve by several reasons. Le me to give some of them:

1. From the theoreticians the dipolar interaction is very complicated because it depends non linearly of the direction besides the distance. Therefore even if we have the same concentration or density of particles the magnetization can be very different due to the configurations that the dipoles have.

2. The experimentalists only consider concentrations of nanoparticles and they don´t distinguish the microscopic the dipole-dipole interaction.

3. On the other hand, if we tried to calculate the dipole-dipole interaction we would face a many-body complicate problem.

4. Measurements of SAR are based in hysteresis losses which which correspond to large number of the magnetization associated to the variation of the magnetic dipoles under a variational magnetic field. Obviously this is also a "macroscopic" measurement which cannot say anything of the individual dipole-dipole interaction.

Part of the explanation for a difference of opinion is because magnetic dipole-dipole interaction energy loss depends upon the local environment of the dipole itself.   

@Diane,

That is true, but oversimplified. The charge interaction also depends of the local environment, but only through Coulomb's law which depends linearly of the distance, while the dipole interaction depends besides non-linearly of the direction. This makes a great difference.

But if you put also the interaction of many different magnetic nanoparticles with different sizes, you can imagine what complex problem arise.

Dear Aslibeiki,

I have just come aware of this old question... Adding to the former comments, I would suggest you this reference 

http://pubs.acs.org/doi/abs/10.1021/acs.jpcc.5b02555

which helps to explain most of the literature within the topic of hyperthermia induced by magnetic nanoparticles. In summary,  a single picture accounts for both the intrinsic magnetic features of the particles (anisotropy, magnetization) and experimental conditions (concentration, magnetic field). Within thsi picture, enhancement and/or decrease of the heating power (SAR) are concomitant with a non-monotonic concentration (i.e. dipolar intensity) dependence

Dear Carlos Martínez-Boubeta,

Thanks for the paper. I already read a paper in which you claimed that that increasing interactions strength will reduce the hypermedia output.

http://scitation.aip.org/content/aip/journal/jap/108/7/10.1063/1.3488881

Also different papers with different results were published in this field.

It seems in the recent research you found an optimum particles concentration with highest hypermedia efficiency.