  The Mermin-Wagner theorem states that long-range magnetic order does not
exist in one- or two-dimensional (2D) isotropic magnets with short-ranged
interactions. The theorem has been a milestone in magnetism and has been
driving the research of recently discovered 2D van der Waals (vdW) magnetic
materials from fundamentals up to potential applications. In such systems, the
existence of magnetic ordering is typically attributed to the presence of a
significant magnetic anisotropy, which is known to introduce a spin-wave gap
and circumvent the core assumption of the theorem. Here we show that in
finite-size 2D vdW magnets typically found in lab setups (e.g., within
millimetres), short-range interactions can be large enough to allow the
stabilisation of magnetic order at finite temperatures without any magnetic
anisotropy for practical implementations. We demonstrate that magnetic ordering
can be created in flakes of 2D materials independent of the lattice symmetry
due to the intrinsic nature of the spin exchange interactions and finite-size
effects in two-dimensions. Surprisingly we find that the crossover temperature,
where the intrinsic magnetisation changes from superparamagnetic to a
completely disordered paramagnetic regime, is weakly dependent on the system
length, requiring giant sizes (e.g., of the order of the observable universe
~10$^{26}$ m) in order to observe the vanishing of the magnetic order at
cryogenic temperatures as expected from the Mermin-Wagner theorem. Our findings
indicate exchange interactions as the main driving force behind the
stabilisation of short-range order in 2D magnetism and broaden the horizons of
possibilities for exploration of compounds with low anisotropy at an atomically
thin level.
