The idea of creating a specifically 'Libertarian Socialist' society is counter-productive and adds to more division where the opposite needs to occur.
All genuine Socialists advocate the same thing – the means of production being put into the hands of the vast majority of people; the working class. There is no need for creating sub-societies for specific tendencies.
I would argue the Socialist Society which exists, is overwhelmingly built up of social-democrats – who are Capitalists.
According to the Oxford Dictionary Definition, Socialism is;
‘a political and economic theory of social organization which advocates that the means of production, distribution, and exchange should be owned or regulated by the community as a whole.’
I hope that shuts up those who were about to come in and start claiming they are Socialists, or that the Soviet Union was Communist.